Algebraic modifications to second quantization for non‐Hermitian complex scaled hamiltonians with application to a quadratically convergent multiconfigurational self‐consistent field method

The algebraic structure for creation and annihilation operators defined on orthogonal orbitals is generalized to permit easy development of bound‐state techniques involving the use of non‐Hermitian Hamiltonians arising from the use of complex‐scaling or complex‐absorbing potentials in the treatment of electron scattering resonances. These extensions are made possible by an orthogonal transformation of complex biorthogonal orbitals and states as opposed to the customary unitary transformation of real orthogonal orbitals and states and preserve all other formal and numerical simplicities of existing bound‐state methods. The ease of application is demonstrated by deriving the modified equations for implementation of a quadratically convergent multiconfigurational self‐consistent field (MCSCF) method for complex‐scaled Hamiltonians but the generalizations are equally applicable for the extension of other techniques such as single and multireference coupled cluster (CC) and many‐body perturbation theory (MBPT) methods for their use in the treatment of resonances. This extends the domain of applicability of MCSCF, CC, MBPT, and methods based on MCSCF states to an accurate treatment of resonances while still using L² real basis sets. Modification of all other bound‐state methods and codes should be similarly straightforward. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Acceleration of self‐consistent field convergence in ab initio molecular dynamics simulation with multiconfigurational wave function

The Lagrange interpolation of molecular orbital (LIMO) method, which reduces the number of self‐consistent field iterations in ab initio molecular dynamics simulations with the Hartree–Fock method and the Kohn–Sham density functional theories, is extended to the theory of multiconfigurational wave functions. We examine two types of treatments for the active orbitals that are partially occupied. The first treatment, as denoted by LIMO(C), is a simple application of the conventional LIMO method to the union of the inactive core and the active orbitals. The second, as denoted by LIMO(S), separately treats the inactive core and the active orbitals. Numerical tests to compare the two treatments clarify that LIMO(S) is superior to LIMO(C). Further applications of LIMO(S) to various systems demonstrate its effectiveness and robustness. © 2014 Wiley Periodicals, Inc.     

RNA secondary structure prediction using a self‐consistent mean field approach

We propose a method for predicting RNA base pairing which imposes no restrictions on the order of base pairs, allows for pseudoknots and runs in O(mN²) time for N base pairs and m iterations. It employs a self‐consistent mean field method in which all base pairs are possible, but with each iteration, the most energetically favored base pairs become more likely as long as they are consistent with their neighbors. Performance was compared against three other programs using three test sets. Sensitivity varied from 20% to 74% and specificity from 44% to 77% and generally, the method predicts too many base pairs leading to good sensitivity and worse specificity. The predicted structures have excellent energies suggesting that, algorithmically, the method performs well, but the classic literature energy models may not be appropriate when pseudoknots are permitted. Website and source code for the simulations are available at http://cardigan.zbh.uni‐hamburg.de/～rnascmf . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Resonances and pseudoresonances in a potential with attractive coulomb tail: A study using analytic‐continuation techniques

The performance of the complex absorbing potential (CAP) and the complex scaling (CS) methods in the detection and calculation of complex Siegert energies is studied using a 1‐D long‐range attractive model potential. This potential is constructed to mimic molecular properties, in particular an attractive Coulombic term, to allow one to draw conclusions on molecular ab initio studies. Analyzing the spectrum of the model potential, one compact bound state embedded in the manifold of Rydberg states is found that shows artificial resonance characteristics when applying the CAP and the CS methods. This pseudoresonance problem is less pronounced in the calculation using the CS method than in that using the CAP method. Despite this deficiency, the CAP method is shown to possess advantages over CS when dealing with physical resonances under conditions that simulate the application of standard basis sets in ab initio calculations. The accuracy of the Siegert energy is shown to be maintained when applying a subspace projection technique to the CAP method. This technique reduces the computational demand significantly and leads to an important improvement of the CAP method, which should be of particular significance in molecular applications. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

The role of resonances in building cross sections: The Mittag‐Leffler expansion in a two‐channel scattering

The Mittag‐Leffler formalism for identifying resonance contributions to a two‐body scattering cross section is extended here from the one channel case to the two channel case. The reduced partial wave cross sections based on subtracting S‐matrix residues are compared with expressions which can be derived from the Breit‐Wigner approximation. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Role of the one‐body Jastrow factor in the transcorrelated self‐consistent field equation

The one‐body Jastrow factor has been introduced into the transcorrelated variational Monte Carlo (TC‐VMC) method. The principal role of the one‐body Jastrow factor in the Jastrow–Slater‐type wave function is to prevent an unfavorable effect of the two‐body Jastrow factor that alters the charge density. In the TC‐VMC method, since the one‐body orbitals are optimized by the transcorrelated self‐consistent field (TC‐SCF) equations, which take into account the electron–electron correlation interactions originating from the two‐body Jastrow factor, the unfavorable effect of altering charge density can be avoided without introducing the one‐body Jastrow factor. However, it is found that it is still better to incorporate a one‐body Jastrow factor into the TC‐VMC method for the practical effect of reducing numerical errors caused by the Monte Carlo sampling and the re‐weighting calculations in solving the TC‐SCF equations. Moreover, since the one‐body Jastrow function adopted in the present work is constructed from the two‐body Jastrow factor without increasing any variational parameter, the computational cost is not significantly increased. The preferable effect of the use of the one‐body Jastrow factor in the TC‐VMC calculation is demonstrated for atoms. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Implementation of the diagonalization‐free algorithm in the self‐consistent field procedure within the four‐component relativistic scheme

A recently developed Thouless‐expansion‐based diagonalization‐free approach for improving the efficiency of self‐consistent field (SCF) methods (Noga and ?imunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four‐component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four‐component diagonalization‐free SCF calculations on several heavy‐metal complexes, the largest of which contains more than 80 atoms (about 6000 4‐spinor basis functions). The diagonalization‐free procedure is about twice as fast as the corresponding diagonalization. © 2014 Wiley Periodicals, Inc.     

New procedure to evaluate aromaticity at the density functional theory,Hartree–Fock,and post‐self‐consistent field levels

The spatial exchange interaction, arising from the exchange‐type two‐electron integrals ( ) between two different groups P and Q, is another driving force for the delocalization of π‐electrons besides orbital charge‐transfer and exchange interactions. We have developed a new combination program for restricted geometry optimization, in which all of the orbital and spatial interactions among isolated groups were excluded from the localized geometry of a conjugated molecule. This was achieved by deleting particular Fock elements and the 15 types of exchange‐type two‐electron integrals, ensuring that the corresponding π‐electrons are completely localized within their respective groups and the π‐orbitals are fully localized. The extra stabilization energy (ESE) of benzene is ?36.3 kcal/mol (B3LYP/6‐31G*), and the level of density functional theory, Hartree–Fock, and post‐self‐consistent field (Møller–Plesset 2, configuration interaction singles and doubles, and singles and doubles coupled‐cluster) and the basis sets have slight effect on the ESE. Based on the comparisons between our procedure, Morokuma's energy decomposition analysis and the block‐localized wave function method, it was confirmed that our program calculates reliable results. The nonaromaticity of acyclic polyenes and antiaromaticity of cyclobutadiene and planar cyclooctatetraene were also estimated. Comparison of the C? C single bond lengths in the ground state with its π‐localized geometries showed that shortening of the single bonds in acyclic polyenes and butadiyne should be attributed to different hybridization, demonstrating that the effect of π‐delocalization on single bonds is so small as to be negligible. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Three‐dimensional reference interaction site model self‐consistent field analysis of solvent and substituent effects on the absorption spectra of Brooker's merocyanine

Solvent and substituent effects on the absorption spectra of Brooker's merocyanine (BM) are investigated using the three‐dimensional reference interaction site model self‐consistent field method and time‐dependent density functional theory. The π–π* excitation energies are computed for BM and its derivative 2,6‐di‐tert‐butyl (di‐t‐Bu) BM. The behaviors of the computed excitation energies with increasing solvent polarity are in good agreement with those of the corresponding experimental measurements. In addition, analysis of the solute–solvent interaction energies and spatial distribution functions reveals that the effects of the solvent on the absorption spectra are reduced by the steric hindrance of the t‐Bu groups. Furthermore, from the difference in the solute–solvent interaction energies of BM and di‐t‐Bu BM, it is shown that the effect of the t‐Bu substituents on the absorption spectrum is greater in high‐polarity solvents. © 2015 Wiley Periodicals, Inc.     

Simulation study of aggregate morphologies formed by ABC linear triblock copolymers in a selective solvent through the self‐consistent field theory

The effect of the hydrophobic properties of blocks B and C on the aggregate morphologies formed by ABC linear triblock copolymers in selective solvent was studied through the self‐consistent field theory. Five typical micelles, such as core‐shell‐corona, hamburger‐like, segmented‐wormlike, were obtained by changing the hydrophobic properties of blocks B and C. The simulation results indicate that the shape and size of micelle are basically controlled by the hydrophobic degree of the middle block B, whereas the type of micelle is mainly determined by the hydrophobic degree of the end block C. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 484–492, 2009     

Controlled self‐assembly of porphyrin/fullerene donor–acceptor complex in a polymer thin film

Thin films composed of polycyclohexane (PCHE), zinc(II)‐5,10,15,20‐tetra‐(2‐naphthyl)porphyrin (ZnTNpP), and [6,6]‐phenyl‐C₆₁‐butyric acid methyl ester (PCBM) blends are prepared to investigate their potential for the controlled self‐assembly of a porphyrin/fullerene donor–acceptor complex in a polymer thin film. The compatibilities of PCHE/PCBM (p), PCHE/ZnTNpP (q), and ZnTNpP/PCBM (r) in these blends have a significant effect on the dispersion of the ZnTNpP/PCBM donor–acceptor complex in the PCHE thin film. When the compatibilities are p << q, r, and q ≈ r, the ZnTNpP/PCBM donor–acceptor complex is formed between the PCHE and PCBM phases. This concept to form a controlled self‐assembly of the ZnTNpP/PCBM donor–acceptor complex may be applied to various combinations of porphyrin/fullerene systems in polymer thin film solar cells to achieve excellent performance. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 743–746     

Molecular dynamics simulations of the Hras‐GTP complex and the Hras‐GDP complex

We study the structures of the Hras‐GTP complex and the Hras‐GDP complex in water to investigate the mechanism of GTP hydrolysis of the Hras‐GTP complex. We performed molecular dynamics simulations of these complexes to investigate the structures of these complexes using the potential parameters of AMBER ff03 and our potential parameters around Mg²⁺. Our simulations show that the averaged structure differences between the Hras‐GTP complex and Hras‐GDP complex are found in the switch I and II regions. In particular, in the switch II region, the α2 ‐ helix of Hras‐GDP is shorter than the α2 ‐ helix of Hras‐GTP. The averaged number of water molecules in the first hydration sphere in Hras‐GDP complex is larger than that in Hras‐GTP complex. The occurrence ratio of the duration time of waters in the first hydration sphere of PA has long tail both in Hras‐GTP and in Hras‐GDP. In Hras‐GDP complex, β‐phosphate is hard to be hydrolyzed, while the number of waters in the first hydration sphere is larger than those in Hras‐GTP. This suggests that there is a special direction for the hydrolysis. © 2013 Wiley Periodicals, Inc.     

The interaction of a novel ruthenium (II) complex with self‐assembled DNA film on silicon surface

Calf thymus DNA (ct‐DNA) films were immobilized onto patterned silicon wafers through electrostatic self‐assembly technology and interacted with a novel dinuclear ruthenium (II) complex, [(bpy)₂Ru(H₂bpi)Ru(bpy)₂](ClO₄)₄, which were demonstrated by using a confocal optical microscope. The morphology of the DNA film was measured by atomic force microscopy and the results show that the DNA strands have been folded into coiled conformations and aggregated into circles with diameters between 18 and 55 nm. The interaction process was also monitored by UV‐visible and fluorescence spectra and investigated by X‐ray photoelectron spectra. The results show that the Ru (II) complex interacts with ct‐DNA by the intercalative mode as it behaves in aqueous solutions. Copyright © 2006 John Wiley & Sons, Ltd.     

Highly effective hydration of olefins using a wool‐palladium complex as a catalyst

The hydration of styrene, 2‐cyclohexen‐1‐one and 5‐hexen‐2‐one to α‐methylbenzyl alcohol, 3‐hydroxy‐cyclohexanone and 5‐hydroxy‐2‐hexanone was investigated using a wool‐supported palladium catalyst under mild conditions of temperature and pressure. The yields amounted to 82.0, 92.0 and 99.3% respectively and were greatly affected by the palladium content in the complex, the ratio of substrate/catalyst, the reaction temperature and the kind of solvent. The catalyst was very stable and could be re‐used several times without any remarkable change in the catalytic activity. Copyright © 2006 John Wiley & Sons, Ltd.     

Mechanistic investigation of vibrational fine structure in e‐H2 scattering using local complex potential‐based time dependent wave packet approach

The structural features of vibrational excitation cross‐sections in resonant e‐H₂ scattering have been investigated using a time dependent wave packet approach and a local complex potential to describe the ²Σ H anion. An analysis of the partial contributions to the vibrational excitation cross‐sections reveals that all features of the excitation profile result from simple interference between bound vibrational levels of H₂ and H. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Oxidation of sulfides including DBT using a new vanadyl complex of a non‐innocent o‐aminophenol benzoxazole based ligand

Reaction of a non‐innocent o‐aminophenol benzoxazole based ligand HL^BAP with VOCl₃ afforded a vanadyl complex, VOL^BIS (SQ), in which SQ is a 2,4‐di‐tert‐butylsemiquinone produced from hydrolysis of HL^BAP. The crystal structure of VOL^BIS (SQ) exhibits an octahedral geometry with the VO²⁺ center coordinated by two nitrogen and one oxygen atoms of L^BAP and two oxygen atoms of SQ. Electrochemical studies showed quasi‐reversible metal‐centered reduction and ligand‐centered oxidation of complex. The magnetic moment of VOL^BIS (SQ) is consistent with the spin‐only value expected for S = 1/2 system. The neutral species of VOL^BIS (SQ) is EPR active, which is consistent with a paramagnetic electronic ground state (S = 1/2). This result is in accordance with the vanadyl (IV) moiety surrounded by tridentate iminobenzosemiquinonate anion radical (HL^BIS)^?‐ and benzosemiquinone ligand (SQ)^?. The theoretical calculations confirm the experimental results. Furthermore, we present the optimal conditions for maximum efficiency of sulfide oxidation for oxidative desulfurization with hydrogen peroxide and 6 times reusability of catalyst for sulfoxidation of dibenzothiophene.     

Design of a reaction field using a linear‐combination‐based isotropic periodic sum method

In our previous study (Takahashi et al., J. Chem. Theory Comput. 2012, 8, 4503), we developed the linear‐combination‐based isotropic periodic sum (LIPS) method. The LIPS method is based on the extended isotropic periodic sum theory that produces a ubiquitous interaction potential function to estimate homogeneous and heterogeneous systems. The LIPS theory also provides the procedure to design a periodic reaction field. To demonstrate this, in the present work, a novel reaction field of the LIPS method was developed. The novel reaction field was labeled LIPS‐SW, because it provides an interaction potential function with a shape that resembles that of the switch function method. To evaluate the ability of the LIPS‐SW method to describe in homogeneous and heterogeneous systems, we carried out molecular dynamics (MD) simulations of bulk water and water–vapor interfacial systems using the LIPS‐SW method. The results of these simulations show that the LIPS‐SW method gives higher accuracy than the conventional interaction potential function of the LIPS method. The accuracy of simulating water–vapor interfacial systems was greatly improved, while that of bulk water systems was maintained using the LIPS‐SW method. We conclude that the LIPS‐SW method shows great potential for high‐accuracy, high‐performance computing to allow large scale MD simulations. © 2014 Wiley Periodicals, Inc.