Chiral Asymmetry and the Spectral Action

We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter

The Holst Action by the Spectral Action Principle

We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.Comment: We correct a sign mistake in Proposition 2.3. As a consequence the main result (Theorem 3.4) becomes more natura

The Chirped Pulse, Fourier Transform Microwave Spectrum Of 1-chloromethyl-1-fluorosilacyclopentane

The microwave spectrum of 1-chloromethyl-1-fluorosilacyclopentane has been recorded for the first time using the chirped pulse, Fourier transform microwave technique. Quantum chemical calculations show the two lowest energy conformers as being a twist-trans and a gauche form with the gauche form previously being shown as having two separate conformations, a gauche+ (lower in energy) and gauche- (higher in energy) form. Analysis of the spectrum provided the observation of the twist-trans conformer only, with 253 and 85 transitions being assigned to the 35Cl and 37Cl isotopologues, respectively. R-branch, a- and b-type transitions were observed. The spectrum was fit to a Watson S-reduced Hamiltonian and consisted of rotational constants, quartic centrifugal distortion constants, and nuclear quadrupole coupling constants, including the determination of the off-diagonal nuclear quadrupole coupling constant, χab. Interpretation of the structure was provided using second moments and is found to have a similar ring structure to other known silacyclopentanes. Analysis of the χzz has been carried out and compared to other similar molecules. An investigation of the known quantum chemical energies of the gauche conformer reveals that the reported B3LYP energies do not align with the observed microwave results

Magnetic Circular Dichroism Spectrum of the Molybdenum(V) Complex [Mo(O)Cl₃dppe]: <i>C</i>-Term Signs and Intensities for Multideterminant Excited Doublet States

The molybdenum­(V) complex [Mo­(O)­Cl₃dppe] [dppe = 1,2-bis­(diphenylphosphino)­ethane] is considered as a model system for a combined study of the electronic structure using UV/vis absorption and magnetic circular dichroism (MCD) spectroscopy. In order to determine the signs and MCD <i>C</i>-term intensities of the chlorido → molybdenum charge-transfer transitions, it is necessary to take the splitting of the excited doublet states into sing-doublet and trip-doublet states into account. While transitions to the sing-doublet states are electric-dipole-allowed, those to the trip-doublet states are electric-dipole-forbidden. As spin–orbit coupling within the manifold of sing-doublet states vanishes, configuration interaction between the sing-doublet and trip-doublet states is required to generate the MCD <i>C</i>-term intensity. The most prominent feature in the MCD spectrum of [Mo­(O)­Cl₃dppe] is a “double <i>pseudo-A</i> term”, which consists of two corresponding <i>pseudo-A</i> terms centered at 27000 and 32500 cm^–1. These are assigned to the ligand-to-metal charge-transfer transitions from the p_π orbitals of the equatorial chlorido ligands to the Mo d_<i>yz</i> and d_<i>xz</i> orbitals. On the basis of the theoretical expressions developed by Neese and Solomon (<i>Inorg. Chem.</i> <b>1999</b>, <i>38</i>, 1847−1865), a general treatment of the MCD <i>C</i>-term intensity of these transitions is presented that explicitly considers the multideterminant character of the excited states. The individual MCD signs are determined from the corresponding transition densities derived from the calculated molecular orbitals of the title complex (BP86/LANL2DZ)