Intermediate Electrostatic Field for the Generalized Elongation Method

An intermediate electrostatic field is introduced to improve the accuracy of fragment‐based quantum‐chemical computational methods by including long‐range polarizations of biomolecules. The point charge distribution of the intermediate field is generated by a charge sensitivity analysis that is parameterized for five different population analyses, namely, atoms‐in‐molecules, Hirshfeld, Mulliken, natural orbital, and Voronoi population analysis. Two model systems are chosen to demonstrate the performance of the generalized elongation method (ELG) combined with the intermediate electrostatic field. The calculations are performed for the STO‐3G, 6‐31G, and 6‐31G(d) basis sets and compared with reference Hartree–Fock calculations. It is shown that the error in the total energy is reduced by one order of magnitude, independently of the population analyses used. This demonstrates the importance of long‐range polarization in electronic‐structure calculations by fragmentation techniques.     

Performance of the elongation method with larger basis sets

The elongation method proposed by Imamura serves as a theoretical model for polymerization processes. It can now be used together with larger basis sets, Hartree–Fock and density functional methods from the Gaussian 94 package with direct self‐consistent field (SCF). This allows electronic structure calculation of elongating clusters with an efficiency superior to full cluster calculations and a precision superior to previous versions of our elongation method. Performance and accuracy compared with full cluster calculations on a regular polymer using the BLYP/6‐31G(d, p) method. Interaction energies of water and hydrogen fluoride polymers of increasing length are compared between HF, BLYP methods and 4‐31G, 6‐31G(d, p) basis sets: Diffuse and polarization functions have a large influence on the interaction energy on both polymers. Local density of states are calculated for different cluster lengths. They are in good agreement with full cluster calculations. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 35–47, 1999     

Highly accurate O(N) method for delocalized systems

The elongation method, developed in our groups, is an ab initio method approaching order O(N) type scalability with high efficiency and high accuracy (error <10^?8?au/atom in total energy compared to the conventional calculation) that can be applied to any one-dimensional (polymer), two-dimensional (surface) or three-dimensional (solid material) systems. For strongly delocalized systems, however, the accuracy of the original elongation method for the targeted entire systems declines by approximately two orders of magnitude in the total energy as compared to the value obtained by the earlier implemented version of the elongation method for nondelocalized systems. The relatively small differences (10^?6?C10^?8 au) between the elongation method and conventional method total energies have caused more serious errors in the second hyperpolarizability, ??, especially in nano-scale systems which have accompanying strong delocalization. In order to solve this problem, we have incorporated a simple correction technique based on an additional ??orbital basis?? to the ??region basis?? in our original elongation method procedures. Some not so-well-localized orbitals are incorporated into the interaction with the attacking molecule. This treatment has been applied to some model nano- and bio-systems that previously have shown strong delocalization, and the high accuracy in the energy obtained for nonstrongly delocalized systems was retained even for the strongly delocalized systems, both for the energies and for the second hyperpolarizabilities. This is a major breakthrough and now expands the systems for which the elongation method can be used to calculate and predict second-order nonlinear optical properties for delocalized systems.     

Elongation method with intermediate mechanical and electrostatic embedding for geometry optimizations of polymers

The elongation method with intermediate mechanical and electrostatic embedding (ELG-IMEE) is proposed. The electrostatic embedding uses atomic charges generated by a charge sensitivity analysis (CSA) method and parameterized for three different population analyses, namely, the Merz–Singh–Kollman scheme, the charge model 5, and the atomic polar tensor. The obtained CSA models were tested on two model systems. Test calculations show that the electrostatic embedding provides several times of decrease in the difference of energies of testing and reference calculations in comparison with the conventional elongation approach (ELG). The mechanical embedding is implemented in a combination of the conventional elongation method and the ONIOM approach. Moreover, it was demonstrated that the geometry optimization with the ELG-IMEE reduces the errors in the optimized structures by about one order in root-mean-square deviation, when compared to ELG.     

LAND-map, a linearized approach to nonadiabatic dynamics using the mapping formalism

We present a new approach for calculating quantum time correlation functions for systems whose dynamics exhibits relevant nonadiabatic effects. The method involves partial linearization of the full quantum path-integral expression for the time correlation function written in the nonadiabatic mapping Hamiltonian formalism. Our analysis gives an algorithm which is both numerically efficient and accurate as we demonstrate in test calculations on the spin-boson model where we find results in good agreement with exact calculations. The accuracy of our new approach is comparable to that of calculations performed using other approximate methods over a relatively broad range of model parameters. However, our method converges relatively quickly when compared with most alternative schemes. These findings are very encouraging in view of the application of the new method for studying realistic nonadiabatic model problems in the condensed phase.     

A new localization scheme for the elongation method

A different localization scheme for the elongation method is developed based on regional molecular orbitals. This scheme is more efficient and more accurate than the previous one especially for covalently bonded systems with strongly delocalized pi electrons. Ab initio test calculations have been performed on three model systems: water chains, polyglycine, and cationic cyanine chains. The dependence on the size of the starting clusters and the effect of the basis set are investigated. Our results are compared with conventional ab initio calculations and it is found in all cases that the error per added unit levels off to a satisfactorily small value as long as the starting cluster is sufficiently large.     

Elongation method for calculating excited states of aromatic molecules embedded in polymers

Photophysical properties of polyethylene structures embedding aromatic fragments (benzene, anthracene, 4‐dicyanomethylene‐4H‐pyran, tryptophan, and estradiol) responsible for existence lowest electronically excited states were studied by new technique involving the elongation method applied to quantum‐chemical calculations. Absorption spectra and some photophysical properties were obtained. The comparison between the elongation and the conventional calculations was made, and it is shown that the elongation method is a powerful tool to determine the excited states as well as optical properties for large systems. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Elongation method for electronic structure calculations of random DNA sequences

We applied ab initio order‐N elongation (ELG) method to calculate electronic structures of various deoxyribonucleic acid (DNA) models. We aim to test potential application of the method for building a database of DNA electronic structures. The ELG method mimics polymerization reactions on a computer and meets the requirements for linear scaling computational efficiency and high accuracy, even for huge systems. As a benchmark test, we applied the method for calculations of various types of random sequenced A‐ and B‐type DNA models with and without counterions. In each case, the ELG method maintained high accuracy with small errors in energy on the order of 10^?8 hartree/atom compared with conventional calculations. We demonstrate that the ELG method can provide valuable information such as stabilization energies and local densities of states for each DNA sequence. In addition, we discuss the “restarting” feature of the ELG method for constructing a database that exhaustively covers DNA species. © 2015 Wiley Periodicals, Inc.     

Development of the cyclic cluster model formalism for Kohn-Sham auxiliary density functional theory methods

The development of the cyclic cluster model (CCM) formalism for Kohn-Sham auxiliary density functional theory (KS-ADFT) methods is presented. The CCM is a direct space approach for the calculation of perfect and defective systems under periodic boundary conditions. Translational symmetry is introduced in the CCM by integral weighting. A consistent weighting scheme for all two-center and three-center interactions appearing in the KS-ADFT method is presented. For the first time, an approach for the numerical integration of the exchange-correlation potential within the cyclic cluster formalism is derived. The presented KS-ADFT CCM implementation was applied to covalent periodic systems. The results of cyclic and molecular cluster model (MCM) calculations for trans-polyacetylene, graphene, and diamond are discussed as examples for systems periodic in one, two, and three dimensions, respectively. All structures were optimized. It is shown that the CCM results represent the results of MCM calculations in the limit of infinite molecular clusters. By analyzing the electronic structure, we demonstrate that the symmetry of the corresponding periodic systems is retained in CCM calculations. The obtained geometric and electronic structures are compared with available data from the literature.     

Electronic structures of large,extended, nonperiodic systems by using the elongation method: Model calculations for the cluster series of a polymer and the molecular stacking on a surface

The elongation method based on the molecular orbital (MO ) theory, which enables us to extend a polymer with any molecular fragments theoretically, has recently been developed by our group. As the next step, we introduced an approach based on the crystal orbital (CO ) theory into above treatment. In the present work, the elongation method was developed at the Hartree–Fock level with CNDO /2 parameters and applied to model systems composed of the cluster series of a polymer and the molecular stacking on a surface. In the cluster-series calculations, the hydrogen molecule [(H₂)_n], hydrogen fluoride [(HF)_n], polyethylene, and polyacetylene were created successively to approximate their one-dimensional periodic polymers by using the MO -based elongation method. In the molecular-stacking models, we described the hypothetical surface of crystal as periodically arranged hydrogen molecules by the CO s, and several hydrogen molecules were stacked up on the surface one after another with the elongation procedure. Furthermore, the lattice defect on surface in which a part of stacked layer is lacking was dealt with by our approach. We also treated carbon monoxide chemisorption on a periodic magnesium chain as a more realistic model. Results for these systems support the applicability of our method for nonperiodic interactions in one- and two-dimensional large systems. © 1995 John Wiley & Sons, Inc.     

The formulation and performance of a perturbative correction to the perfect quadruples model

A recently published alternative hierarchy of coupled-cluster approximations is reformulated as a perturbative correction. A single variant, a model for the total electronic energy based on the perfect quadruples model, is explored in detail. The computational scaling of the method developed is the same as canonical second order Mo?ller-Plesset perturbation theory (fifth order in the number of molecular orbitals), but its accuracy competes with the high-accuracy, high-cost standard CCSD(T), even when the latter is allowed to break spin-symmetry. The variation presented can be implemented without explicit calculation and storage of the most expensive energy contributions, thereby improving the range of systems which can be treated. The performance and scaling of the method are demonstrated with calculations on the water, fluorine, and oxirane molecules, and compared to the parent model.     

Flexible effective fragment QM/MM method: validation through the challenging tests

A new version of the QM/MM method, which is based on the effective fragment potential (EFP) methodology [Gordon, M. et al., J Phys Chem A 2001, 105, 293] but allows flexible fragments, is verified through calculations of model molecular systems suggested by different authors as challenging tests for QM/MM approaches. For each example, the results of QM/MM calculations for a partitioned system are compared to the results of an all-electron ab initio quantum chemical study of the entire system. In each case we were able to achieve approximately similar or better accuracy of the QM/MM results compared to those described in original publications. In all calculations we kept the same set of parameters of our QM/MM scheme. A new test example is considered when calculating the potential of internal rotation in the histidine dipeptide around the C(alpha)bond;C(beta) side chain bond.     

On the accuracy of correlation-energy expansions in terms of local increments

The incremental scheme for obtaining the energetic properties of extended systems from wave-function-based ab initio calculations of small (embedded) building blocks, which has been applied to a variety of van der Waals-bound, ionic, and covalent solids in the past few years, is critically reviewed. Its accuracy is assessed by means of model calculations for finite systems, and the prospects for applying it to delocalized systems are given.     

Improved Wang-Landau sampling through the use of smoothed potential-energy surfaces

A method is presented to improve the speed of convergence of Wang-Landau simulations as used to calculate the density of states of continuous systems. The density of states is first crudely estimated with calculations employing a smoothed potential-energy surface. This estimate is then used as a seed for subsequent Wang-Landau simulations using the original potential. The performance of the method is demonstrated by employing several simple models, including an analytically solvable harmonic system as well as a Go model of a protein. For all systems considered, the seeded simulations were found to converge significantly faster and with higher accuracy than the standard Wang-Landau simulations.     

Modelling of high-pressure phase equilibria using the Sako–Wu–Prausnitz equation of state: II. Vapour–liquid equilibria and liquid–liquid equilibria in polyolefin systems

Phase equilibria in binary and ternary polyolefin systems are calculated using the cubic equation of state proposed by Sako–Wu–Prausnitz (SWP). Calculations were done for high-pressure phase equilibria in ethylene/polyethylene (LDPE) systems and for liquid–liquid equilibria (LLE) in systems containing either high-density polyethylene or poly(ethylene-co-propylene). The calculations for the copolymer/solvent systems are compared with those using the SAFT EOS. The two equations of state can describe UCST, LCST as well as U-LCST behaviour with similar accuracy. Whereas, the binary interaction parameter is temperature-independent for SAFT, it is found to be a function of temperature for the SWP model. Moreover, the influence of an inert gas on the LCST of the polyethylene/hexane system is investigated using the SWP EOS. The polydispersity of the different polyethylenes is considered in the phase equilibrium calculations using pseudocomponents chosen by the moments of the experimental molecular weight distributions.     

ABEEM浮动电荷分子力场在含离子体系中的发展和应用

离子水合及生物分子体系内离子选择性的微观作用机制是人们长期探索的重要课题,其难点在于如何合理精确地描述上述体系内的离子-水、离子-生物分子等各种相互作用.本文主要总结近年来原子-键电负性均衡浮动电荷分子力场（ABEEM/MM）在含离子体系中的发展和应用,包括离子水溶液、金属蛋白、离子-核酸碱基体系的研究.我们优选相关参数,构建上述体系的势能函数,并对气相水合离子团簇、离子水溶液、金属蛋白、离子-核酸碱基体系进行研究,模拟其结构、活性、热力学和动力学等性质.研究和比较结果表明,我们的ABEEM浮动电荷力场总体上优于其它力场方法,其精度可达到或接近高水平从头计算MP2方法.这为进一步探讨生物分子体系内的离子选择性、金属酶及其它含离子体系的结构和性质奠定了基础.     

Monge-Ampere grids and the multidimensional mapped Fourier method

The efficiency of a numerical method can be greatly improved by combining it with coordinate transformations tailored to a given problem. This is the basis for the mapped Fourier methods. However, obtaining "good" coordinate transformations is a major obstacle for this approach in multidimensions. Here, we calculate coordinate transformations based on solving the Monge-Ampere equation. These transformations are combined in the mapped Fourier method and applied to Schrodinger's equation in multidimensions. Dramatic improvements in accuracy compared to the standard Fourier method were observed in eigenvalue calculations for two-dimensional systems. This work indicates that the Monge-Ampere equation may serve as a useful tool for constructing efficient representations for problems in computational quantum mechanics and other fields.