The Valence Bond Study for Benzenoid Hydrocarbons of Medium to Infinite Sizes

Abstract

The ground-state energies of polyacenes and polyphenanthrenes are obtained with the density-matrix renormalization group method from finite up to infinite lengths under the classical valence bond theory. In comparison with the exact valence bond results, numerical errors of retaining various numbers of states are all less than 10 -5 J. Meanwhile, the linear equations in terms of the chain length are deduced for the groundstate energies of these two homologous series. And the energy gaps between the lowest singlet and triplet states (S-T gap) are also evaluated. On the other hand, the relative local hexagon energy converges as the chain length increases, and leading to an effective conjugated length of n ) 12 for polyacene and polyphenanthrene.

The radical character of the acenes: A density matrix renormalization group study

“…[60][61][62][63][64][65] Recall that we can expand any wave function in terms of resonance structures, which may be classified as covalent, singly ionic, doubly ionic, and so on ͑see Fig. 8͒.…”

HEISENBERG MODEL AND ITS APPLICATIONS TO Π-Conjugated SYSTEMS

“…33 We begin with anthracene. In the first step, we calculate the ground state of anthracene using the Lanczos method.…”

“…We have carried out DMRG calculations on energies of the ground and the first triplet states for two series of polycyclic aromatic hydrocarbons, polyacene (Pac) and polyphenanthrene (Pph), of arbitrary lengths defined by the number of constituent hexagons n (or carbon atoms N = 4n+2). 33 The strategy of choosing the suitable blocks in the DMRG algorithm for these two cata-condensed aromatic systems were introduced in Sec. 3.2.…”

“…Recently, within the Heisenberg model we introduced a scheme of choosing the suitable blocks for cata-condensed aromatic systems and carried out DMRG calculations on energies of the ground and the first triplet states for polyacene (Pac) and polyphenanthrene (Pph) of arbitrary lengths. 33 In comparison with the exact results, numerical errors of the DMRG energies per site are less than 10 −5 J. The saturation of some interesting properties, such as the energy gaps between the lowest singlet and triplet states (S-T gap) and the local aromaticity of constituent hexagons, upon the propagation of Pac and Pph series has been investigated, giving interesting information on understanding the transition from molecules to solids with the Heisenberg model.…”

“…Since the exact solutions of the Heisenberg model have been limited to the conjugated systems of no more than 30 π-electrons on a typical workstation, we must resort to approximate calculation methods for obtaining approximate solutions as accurate as possible. One of the most powerful techniques for studying strongly correlated electron systems, the density-matrix renormalization group (DMRG) method introduced by White, has been shown to be extremely successful in solving the many-electron models for one-dimensional systems, 29 especially the Heisenberg model [29][30][31][32][33] and the Hubbard model. [34][35][36] However, extending DMRG method to quasi-one-dimensional or two-dimensional systems of chemical interests, the exponential decrease of the numerical precision with the increase of the system width makes this method impractical rapidly.…”