A linear-scaling scheme for estimating the electronic energy, gradients, and Hessian of a large molecule at ab initio level of theory based on fragment set cardinality is presented. With this proposition, a general, cardinality-guided molecular tailoring approach (CG-MTA) for ab initio geometry optimization of large molecules is implemented. The method employs energy gradients extracted from fragment wave functions, enabling computations otherwise impractical on PC hardware. Further, the method is readily amenable to large scale coarse-grain parallelization with minimal communication among nodes, resulting in a near-linear speedup. CG-MTA is applied for density-functional-theory-based geometry optimization of a variety of molecules including alpha-tocopherol, taxol, gamma-cyclodextrin, and two conformations of polyglycine. In the tests performed, energy and gradient estimates obtained from CG-MTA during optimization runs show an excellent agreement with those obtained from actual computation. Accuracy of the Hessian obtained employing CG-MTA provides good hope for the application of Hessian-based geometry optimization to large molecules.

The development of a fragmentation-based scheme, viz. molecular tailoring approach (MTA) for ab initio computation of one-electron properties and geometry optimization is described. One-electron properties such as the molecular electrostatic potential (MESP), molecular electron density (MED), and dipole moments are computed by synthesizing the density matrix (DM) of the parent molecule from DMs of its small overlapping fragments. The electron density obtained via MTA was found to be typically within 0.5% of its actual counterpart, while maximum errors of about 2% were noticed in the case of the dipole moment and MESP distribution. An attempt is made to develop MTA-based geometry optimization that involves picking relevant energy gradients from fragment self-consistent field (SCF) calculations, bypassing the CPU and memory extensive SCF step of the complete molecule. This is based on the observation that the MTA gradients mimic the actual ones fairly well. As the calculations on individual fragments are mutually independent, this algorithm is amenable to large-scale parallelization and has been extended to a distributed setup of PCs. The code developed is put to test on γ-cyclodextrin, taxol, and a small albumin-binding protein (1prb) for one-electron properties. Further, molecules such as γ-cyclodextrin, taxol, a silicalite, and 1prb are subjected to MTA-based geometry optimization, on a PC cluster. The results indicate a favorable speedup of two to three times over the actual computations in the initial phase of optimization. Furthermore, it enables computations otherwise not possible on a PC. Preliminary results indicate similar savings with sustained accuracy even for large molecules at the level of Møller–Plesset second order perturbation (MP2) theory.

A linear scaling method, termed as cardinality guided molecular tailoring approach, is applied for the estimation of the Hessian matrix and frequency calculations of spatially extended molecules. The method is put to test on a number of molecular systems largely employing the Hartree-Fock and density functional theory for a variety of basis sets. To demonstrate its ability for correlated methods, we have also performed a few test calculations at the Moller-Plesset second order perturbation theory. A comparison of central processing unit and memory requirements for medium-sized systems with those for the corresponding full ab initio computation reveals substantial gains with negligible loss of accuracy. The technique is further employed for a set of larger molecules, Hessian and frequency calculations of which are not possible on commonly available personal-computer-type hardware.

Single-crystalline novel LaFeO 3 dendritic nanostructures are synthesized by a well-controlled, surfactantassisted facile hydrothermal process. The morphology of the material is investigated by high-resolution transmission and scanning electron microscopy. The crystal nature and chemical composition of LaFeO 3 dendritic nanostructures are revealed from the X-ray diffraction, Raman spectroscopy, and X-ray photoelectron spectroscopy. Structural characterizations imply the preferential growth along the [121] direction by oriented attachment of LaFeO 3 nanoparticles in the diffusion limit, leading to the formation of LaFeO 3 dendrites. The microscopic studies confirm the formation of dendrites with a length of 3−4 μm, a branch diameter of 80 nm, and a length of 1−1.5 μm. The possible growth mechanism of the dendritic morphology is discussed from the aspect of diffusion and oriented attachment based on experimental results. Further, the electrochemical measurements performed on LaFeO 3 dendritic nanostructures deposited on the surface of a glassy carbon electrode exhibit a strong promoting effect. The oxidation current is proportional to concentration in the linear range of 8.2 × 10 −8 to 1.6 × 10 −7 M with a detection limit of 62 nM at S/N = 3. Meanwhile, the sensor effectively avoids the interference of ascorbic acid and uric acid, and it is successfully applied to determine the dopamine formulations with high selectivity and sensitivity.

A completely automated algorithm for performing many-body interaction energy analysis of clusters (MBAC) [M. J. Elrodt and R. J. Saykally, Chem. Rev. 94, 1975 (1994); S. S. Xantheas, J. Chem. Phys. 104, 8821 (1996)] at restricted Hartree-Fock (RHF)/MA Plesset 2nd order perturbation theory (MP2)/density functional theory (DFT) level of theory is reported. Use of superior guess density matrices (DM's) for smaller fragments generated from DM of the parent system and elimination of energetically insignificant higher-body combinations, leads to a more efficient performance (speed-up up to 2) compared to the conventional procedure. MBAC approach has been tested out on several large-sized weakly bound molecular clusters such as (H(2)O)(n), n=8, 12, 16, 20 and hydrated clusters of amides and aldehydes. The MBAC results indicate that the amides interact more strongly with water than aldehydes in these clusters. It also reconfirms minimization of the basis set superposition error for large cluster on using superior quality basis set. In case of larger weakly bound clusters, the contributions higher than four body are found to be repulsive in nature and smaller in magnitude. The reason for this may be attributed to the increased random orientations of the interacting molecules separated from each other by large distances.