A mixed molecular orbital and valence bond (MOVB) method has been developed and applied to chemical reactions. In the MOVB method, a diabatic or valence bond (VB) state is defined with a block-localized wave function (BLW). Consequently, the adiabatic state can be described by the superposition of a set of critical adiabatic states. Test cases indicate the method is a viable alternative to the ...

Rodin and Sullivan (1987) proved Thurston’s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby providing a refreshing geometric view of Riemann’s Mapping Theorem. We now present a new proof of the Rodin–Sullivan theorem. This proof is based on the argument principle, and has the following virtues. 1. It applies to more general packings. The Ro...

The dioxygen molecule has been the subject of valence bond (VB) studies since 1930s, as it was considered as the first "failure" of VB theory. The object of this article is to provide an unambiguous VB interpretation for the nature of chemical bonding of the molecule by means of modern VB computational methods, VBSCF, BOVB, and VBCI. It is shown that though the VBSCF method can not provide quan...

We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the configuration of the valence bonds. This allows us to determine the phase transition point in between different VBS...

Valence bond theory reveals the nature of OC–C in carbon suboxide and related allene compounds.

It is shown how previously reported bond energy equations (Van Hooydonk, 1973) can be re­ generated starting from the assumptions (i) that the valence-orbital energy of an element in a bond can be expressed as a function of its occupancy number (Iczkowski-Margrave, 1961) and (ii) that the potential around an atom in a bond vanishes as soon as its valence orbital is doubly occupied (Ferreira, 19...