An elongation method for large systems toward bio-systems

Abstract

The elongation method, proposed in the early 1990s, originally for theoretical synthesis of aperiodic polymers, has been reviewed. The details of derivation of the localization scheme adopted by the elongation method are described along with the elongation processes. The reliability and efficiency of the elongation method have been proven by applying it to various models of bio-systems, such as gramicidin A, collagen, DNA, etc. By means of orbital shift, the elongation method has been successfully applied to delocalized π-conjugated systems. The so-called orbital shift works in such a way that during the elongation process, some strongly delocalized frozen orbitals are assigned as active orbitals and joined with the interaction of the attacking monomer. By this treatment, it has been demonstrated that the total energies and non-linear optical properties determined by the elongation method are more accurate even for bio-systems and delocalized systems like fused porphyrin wires. The elongation method has been further developed for treating any three-dimensional (3D) systems and its applicability is confirmed by applying it to entangled insulin models whose terminal is capped by both neutral and zwitterionic sequences.

Analytic Gradient for Density Functional Theory Based on the Fragment Molecular Orbital Method

“…For comparison purposes, the error in the numerical gradient is set to zero. To test the accuracy of the gradient for systems with and without fragmentation across a covalent bond, two test systems were chosen: a (H 2 O) 32 cluster (Figure 1a) and an alanine (ALA) 7 polypeptide chain in an α helix configuration (Figure 1b). For both test systems, calculations were performed with several density functionals.…”

“…For the gradient calculations with response terms, U̅ a from eq 24 was included in the gradient. 25,36 The numerical energy gradient was calculated using double differencing with a step size of 0.0001 and 0.0005 Å for the (H 2 O) 32 cluster and the (ALA) 7 polypeptide chain, respectively.…”

Elongation method for electronic structure calculations of random DNA sequences

“…Conversely, several approaches, such as the divide-andconquer method, [13,14] the fragment molecular orbital (MO) method, [15] the systematic fragmentation method, [16] the energybased fragmentation approach, [17,18] quantum fast multiple method, [19,20] and molecular fractionation with conjugate caps, [21] have been proposed for efficient calculations on large systems. For the same purpose, we developed an ab initio order-N [O(N)] elongation (ELG) method [22][23][24][25] based on the concept of a computational polymerization reaction. In this approach, the computation mimics a polymerization process in which the reaction terminal of a main cluster is attacked by monomers step by step to elongate the electronic structure of the system.…”

“…However, the ELG calculation can be expected to be applied to DNAs under water by (1) approximately including only vicinal water molecules in the unit structure, (2) using the continuum solvent model incorporated in the ELG method, [25] and so on.…”

FMO3-LCMO study of electron transfer coupling matrix element and pathway: Application to hole transfer between two tryptophans through cis- and trans-polyproline-linker systems

“…However, first-principles treatment of electrons in large biomolecular systems is still a formidable task. In this regard, fragment-based approaches, such as the fragment molecular orbital (FMO) [7][8][9], Divide-and-Conquer [10,11], and many others [12][13][14][15] appear promising.…”