Hyperconjugation: The Electronic Mechanism That May Underlie the Karplus Curve of Vicinal NMR Indirect Spin Couplings

Polarization propagator theory and the entanglement between MO excitations

Entanglement is at the core of quantum physics and so, one may conjecture that it should have some influence on atomic and molecular response properties. The usual way of treating entanglement is by applying information theory via the von Newman entropy. Given that the principal propagator is the operator that contains the physical information that arises due to the transmission of the effects of two external perturbations through the electronic framework of a quantum system, it should have in it the information necessary to quantify the likely entanglement among molecular orbital excitations. In this article we first propose a proper density matrix and from it, the way to quantify entangled excitations by using information theory. The NMR J-couplings are among the best candidates to learn about the potentialities of this formalism. We applied this new tool to analyze the famous Karplus rule and found a relationship between the dihedral angular dependence and the entanglement. We also found that the entangled excitations are related to electron correlation. The new formalism can be applied to all other response properties.

HYPERCONJUGATION EFFECT ON THE STRUCTURAL STABILITY OF A TERT-BUTYL AND ITS DERIVED C4Hn(n = 4–10) ISOMERS

The hyperconjugation effect on molecular structural stability is studied by performing first-principles calculations on the tert-butyl and its derived C 4 H n(n = 4–10) isomer structures. Four of the isomer structures with n = 7–10 were found to show hyperconjugation similar to that in the tert-butyl, with hyperconjugation orbital energies decreasing with the increase of the number of hydrogen atoms participating in the hyperconjugation (PIH). The distribution of charge carried by the PIH hydrogen atoms is uniform, which reveals a delocalization character in the electronic structures; and the PIH hydrogen atoms are found responsible for the main IR spectrum peak relating to C-H stretching vibration.

Experimental and DFT studies on the transmission mechanisms of analogous NMR JCH and JCC couplings in 1-X- and 1-X-3-methylbicyclo[1.1.1]-pentanes

The main aim of this work is to compare the transmission mechanisms for the Fermi contact term of spin-spin couplings, SSCCs, in series 1-X-bicyclo[1.1.1]-pentane, (1), and 1-X-3-methylbicyclo[1.1.1]pentane, (2), and from that comparison to gain insight into some subtle aspects of the FC transmission. To this end, 18 members of the latter series were isotopically enriched in (13)C at the methyl position and the following couplings were measured; 1JC3CMe, 3JC1CMe and 4JCXCMe. These three types of SSCCs in (2) are compared, respectively, with 1JC3H3, 3JC1H3 and 4JCXH in (1); these latter values were taken from previous works. Since electron delocalization plays an important role in the transmission of the FC interaction, the natural bond orbital (NBO) method is employed to quantify electron delocalization interactions within selected members of series (1) and (2). It is found that 1JC3H3 SSCCs in (1) is more efficiently transmitted than 1JC3CMe SSCCs in (2). On the other hand, 3JC1H3 and 4JCXH SSCCs in (1) are notably less efficiently transmitted than 3JC1CMe and 4JCXCMe SSCCs in (2), although substituent effects on these two SSCCs show the opposite trends. These different efficiencies are rationalized in terms of different sigma-hyperconjugative interactions in both series of compounds.