We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. perform a self-consistent Hartree-Fock that incorporates these effects alongside realistic interaction substrate potentials, explore comprehensive set competing orders including those break translational at arbitrary wavevectors. find all non-zero integer fill...

Two connections between fullerene structures and alternating knots are established. Knots may appear in two ways: from zigzags, i.e., circuits (possibly self-intersecting) of edges running alternately left and right at successive vertices, and from railroads, i.e., circuits (possibly self-intersecting) of edge-sharing hexagonal faces, such that the shared edges occur in opposite pairs. A z-knot...

The seminal discovery in 1865 by Kekulé that benzene nucleus exists with cyclic skeleton is considered to be the beginning of aromatic chemistry. Since then, a myriad of cyclic molecules displaying aromatic property have been synthesized. Meanwhile, borazine (B3N3H6), despite the isostructural and isoelectronic relationships with benzene, exhibits little aromaticity. Herein, we report the synth...

The structure and vibrational frequencies of styrene and trans-b-methyl styrene in the lowest three singlet states ~S0 , S1 , and S2! have been calculated using ab initio quantum chemical methods. The frequencies are compared with experimental data obtained in the bulk and in a supersonic jet. The calculation shows that in the ground state the molecules have a broad shallow potential as a funct...