On the development of exponential ansatze for quantum dynamics in finite dimensional vector spaces

Summary A Wei-Norman type of exponential ansatz is constructed for the time evolution operator in finite dimensional vector spaces. Based on an analysis of the structure of the concerned operator algebra, it is shown that a reduction principle exists even for simple algebras that goes beyond the Wei-Norman result when a specific ordering of the operators is used such that the equations of motion for different generators belonging to different classes are decoupled. It is shown that the solution in this case is global. Some specific approximation schemes are considered and their strengths and weaknesses are analyzed. Model calculations are presented to bring out these features.     

Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: applications to the molecular systems and geometric objects

This article describes a number of algorithms that are designed to improve both the efficiency and accuracy of finite difference solutions to the Poisson-Boltzmann equation (the FDPB method) and to extend its range of application. The algorithms are incorporated in the DelPhi program. The first algorithm involves an efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three-dimensional lattice. This method constitutes a significant improvement over existing methods in terms of its combination of speed and accuracy. The DelPhi program has also been expanded to allow the definition of geometrical objects such as spheres, cylinders, cones, and parallelepipeds, which can be used to describe a system that may also include a standard atomic level depiction of molecules. Each object can have a different dielectric constant and a different surface or volume charge distribution. The improved definition of the surface leads to increased precision in the numerical solutions of the PB equation that are obtained. A further improvement in the precision of solvation energy calculations is obtained from a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies. The program allows for finite difference grids of large dimension; currently a maximum of 571(3) can be used on molecules containing several thousand atoms and charges. As described elsewhere, DelPhi can also treat mixed salt systems containing mono- and divalent ions and provide electrostatic free energies as defined by the nonlinear PB equation.     

Ab initio calculation of electronic circular dichroism fortrans-cyclooctene using London atomic orbitals

Summary The second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the exact operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations ontrans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The rotatory strength calculated fortrans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that oftrans-cyclooctene.Dedicated to Prof. Jan Linderberg     

Summation of the perturbation series for the energy levels of a hydrogen atom in a magnetic field

A new method to sum divergent power series is developed and applied to the calculation of the energy levels of the hydrogen atom in a uniform magnetic field. Analytical expressions for the first two eigenstates obtained in this way are shown to agree closely with accurate numerical calculations in the whole range of field strengths.     

Evaluating Shielding‐Based Ring‐Current Models by Using the Gauge‐Including Magnetically Induced Current Method

Magnetically induced current densities and integrated ring‐current strength susceptibilities have been calculated at the density functional theory (DFT) level for a test set consisting of 17 ring‐shaped molecules using the gauge‐including magnetically induced current (GIMIC) method. Reliable values for the ring‐current strengths have been obtained by performing numerical integration of the current‐density susceptibility passing a cut plane perpendicularly to the molecular ring. The current densities and ring current strengths were calculated at the DFT level using the B3LYP functional and def2‐TZVP basis sets. Current densities and ring‐current strengths have also been calculated at the Hartree‐Fock self‐consistent field (HF‐SCF) level using Dunning’s aug‐cc‐pVTZ basis sets, which allow a direct comparison with ring‐current strengths that have previously been estimated using ring‐current models based on magnetic shielding calculations. Current density calculations at both levels of theory show that the magnetic shielding based ring‐current models are not a very accurate means to estimate the magnetically induced ring current strengths, whereas they provide qualitatively the correct aromaticity trends for the studied molecules.     

Vibrational Stark effect: Theoretical determination through the semiempirical AM1 method

The vibrational Stark effect of a series of small molecules has been calculated by means of the semiempirical AM1 method through addition of the electron–field interaction term in the one-electron Hamiltonian. Optimized geometrical parameters along with harmonic frequencies and line intensities are determined for different strengths of the applied uniform electric field. The perturbed spectra are compared with theoretical studies carried out at the ab initio level and with experimental results. The vibrational Stark effect of the retinal molecule is also computed, showing that this kind of study is feasible in systems of biochemical interest. © 1992 by John Wiley & Sons, Inc.     

Estimations of electric field effects on the oxygen reduction reaction based on the density functional theory

By varying the external electric field in density functional theory (DFT) calculations we have estimated the impact of the local electric field in the electric double layer on the oxygen reduction reaction (ORR). Potentially, including the local electric field could change adsorption energies and barriers substantially, thereby affecting the reaction mechanism predicted for ORR on different metals. To estimate the effect of local electric fields on ORR we combine the DFT results at various external electric field strengths with a previously developed model of electrochemical reactions which fully accounts for the effect of the electrode potential. We find that the local electric field only slightly affects the output of the model. Hence, the general picture obtained without inclusion of the electric field still persists. However, for accurate predictions at oxygen reduction potentials close to the volcano top local electric field effects may be of importance.     

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

Using three typical pi-conjugated molecules (1,3,5-hexatriene, 1-formyl-6-hydroxyhexa-1,3,5- triene, and 1,1-diamino-6,6-dinitrohexa-1,3,5-triene) we investigate the level of ab initio theory necessary to produce reliable values for linear and nonlinear optical properties, with emphasis on the vibrational contributions that are known to be important or potentially important. These calculations are made feasible by employing field-induced coordinates in combination with a finite field procedure. For many, but not all, purposes the MP2/6-31+G(d) level is adequate. Based on our results the convergence of the usual perturbation treatment for vibrational anharmonicity was examined. Although this treatment is initially convergent in most circumstances, a problematic situation has been identified.     

Error analysis and efficient sampling in Markovian state models for molecular dynamics

In previous work, we described a Markovian state model (MSM) for analyzing molecular-dynamics trajectories, which involved grouping conformations into states and estimating the transition probabilities between states. In this paper, we analyze the errors in this model caused by finite sampling. We give different methods with various approximations to determine the precision of the reported mean first passage times. These approximations are validated on an 87 state toy Markovian system. In addition, we propose an efficient and practical sampling algorithm that uses these error calculations to build a MSM that has the same precision in mean first passage time values but requires an order of magnitude fewer samples. We also show how these methods can be scaled to large systems using sparse matrix methods.     

High Electric Field Strengths in Micellar Electrokinetic Capillary Electrophoresis with Ionic Liquids as Modifiers

Abstract

In this study, a method for the separation and determination of basic analytes in aqueous capillary electrophoresis (CE) was developed based on high electric field strengths and ionic liquids (ILs). The resulting electric field strengths ranged from 500 to 1000 V/cm. Trishydroxymethylaminomethane (Tris) and sodium cholate (SC) were used as main electrolytes. The ionic liquids 1‐ethyl‐3‐methylimidazoium tetrafluoroborate (1E‐3MI‐TFB) and 1‐butyl‐3‐methylimidazoium tetrafluoroborate (1B‐3MI‐TFB) were used as modifiers to improve the separation efficiency and selectivity. It was shown that increasing the applied electric field strengths not only caused short analysis time, but also did not induce excessive Joule heating in the capillary when ionic liquids were used as modifiers. The susceptibility to high electric field of separation efficiency in capillary electrophoresis, with the effect of ionic liquids, was subsequently discussed, and the developed method was used to analyze three model analytes in Sinacalia tangutica. The accurate results illustrated that high electric field strength with the ionic liquids was feasible in CE.     

Dynamic intensity model calculation of vibronic oscillator strengths for Cs2NaNdCl6: A molecular dynamics study

We present here a dynamic intensity model calculation of vibronic oscillator strengths for the Cs2NaNdCl6 compound by applying the method of molecular-dynamics simulation (MDS). The force field parameters used for the MDS reproduce the structure and several vibrational frequencies of Cs2NaNdCl6 very well. Both the static-coupling (SC) and dynamic-coupling (DC) mechanisms are taken into account for the intensity parameter calculations, in which the effective point charges and isotropic polarizabilities are optimized with respect to experimental energy levels. A comparison of intensity parameters and vibronic oscillator strengths between the two individual mechanisms indicates that the DC mechanism is operative. The calculated vibronic oscillator strengths for the combined SC and DC mechanism agree quite well with the available experimental values.     

First Principles Calculations of Electric Field Effect on the (6,0) Zigzag Single-Walled Silicon Carbide Nanotube for use in Nano-Electronic Circuits

Structural, electronic, and electrical responses of the H-capped (6,0) zigzag single-walled silicon carbide nanotube (SiCNT) was studied under the parallel and transverse electric fields with strengths 0–140 × 10^?4 a.u. by using density functional calculations. Analysis of the structural parameters indicates that resistance of the nanotube against the applied parallel electric field is more than resistance of the nanotube against the applied transverse electric field. The dipole moments, atomic charge variations, and total energy of the (6,0) zigzag SiCNT show increases with any increase in the applied external electric field strengths. The length, tip diameters, electronic spatial extent, and molecular volume of the nanotube do not change significantly with any increasing in the electric field strength. The energy gap of the nanotube increases with any increases in the electric field strength and its reactivity is decreased. Increase of the ionization potential, electron affinity, chemical potential, and HOMO and LOMO in the nanotube with increase of the applied external electric field strengths indicates that the properties of SiCNTs can be controlled by the proper external electric field for use in nano-electronic circuits.     

Is the trend of the polarizability per atom for all small 3d transition metal clusters the same? The case of Nin (n< or =5) clusters

The first theoretical study on static polarizability and polarizability anisotropy of small nickel clusters up to the pentamer is presented. All-electron-type calculations were performed using a finite field approach as implemented in the density functional program deMon2K. A newly developed first-order field-induced basis set for density functional calculations was employed. For the static polarizability per atom of these clusters, a different trend to the one reported in the literature for other transition metal cluster systems of similar size, is observed.     

The expanding field of SILAC

Stable isotope labeling by amino acids (SILAC) metabolically encodes cell populations for protein quantification by mass spectrometry. SILAC was introduced in 2002 and the field of mass spectrometry based proteomics has changed dramatically over the last decade. Increased sensitivity and speed of mass spectrometry instruments coupled with significantly improved mass resolution and precision have led to much higher rates of peptide identification and deeper coverage of proteomic samples. Several proteomics approaches are now available for quantifying proteins and their post-translational modifications, each with their strengths and weaknesses. The simplicity and robustness of SILAC have led to its widespread adoption and new applications have emerged that play to its particular strengths as a metabolic labeling approach.     

激发态1，2-二硫环丁烯去活性和异构化机理的理论研究

运用完全活性空间多组态CASSCF方法研究了激发态1,2-二硫环丁烯（1,2-Dithiete）势能面交叉机理．自旋．轨道耦合（SOC）常数采用完全Pauli-Breit旋轨耦合算符（包括单电子和双电子项）进行计算,其强度为198．37或211．35cm^-1,对不同自旋态跃迂起着重要作用．研究结果表明：光激发1,3-dithiol-2-one导致形成主要产物trans—dithioglyoxal（Trans-MinS0）和次级产物thiolthioketene．计算与实验观察结果一致．     

Critical conditions for stable dipole-bound dianions

We present finite size scaling calculations of the critical parameters for binding two electrons to a finite linear dipole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. A complete ground state stability diagram for the dipole-bound dianion is obtained using accurate variational and finite size scaling calculations. We also study the near threshold behavior of the ground state energy by calculating its critical exponent.     

Calculated ro-vibrational fine-structure spectrum and weak-field zeeman splittings of the O2Ar van der Waals molecule

Ro-vibrational calculations are performed on O₂Ar explicitly including coupling to the O₂ electronic spin. Two different empirical potentials are used and give similar fine-structure spectra. The anisotropy in the potential is found to strongly perturb the O₂ fine-structure spectrum suggesting that the O₂Ar fine-structure spectrum can give detailed information about the anisotropy of the van der Waals interaction potential. Transition strengths for the complex fine-structure transitions are calculated and found to vary by two orders of magnitude. The Zeeman splitting of the levels by interaction with a weak magnetic field is also calculated.     

A theoretical study of bond selective photochemistry in CH2BrI

Bromoiodomethane photodissociation in the low-lying excited states has been characterized using unrestricted Hartree-Fock, configuration-interaction-singles, and complete active space self-consistent field calculations with the SDB-aug-cc-pVTZ, aug-cc-pVTZ, and 3-21g** basis sets. According to the results of the vertical excited energies and oscillator strengths of these low-lying excited states, bond selectivity is predicted. Subsequently, the minimum energy paths of the first excited singlet state and the third excited state for the dissociation reactions were calculated using the complete active space self-consistent field method with 3-21g** basis set. Good agreement is found between the calculations and experimental data. The relationships of excitations, the electronic structures at Franck-Condon points, and bond selectivity are discussed.     

Nematic-fluid structure in wall-field geometry. II. The direct correlation function

An explicit expression for the wall-nematic direct correlation function (DCF) is obtained for any orientation of the wall with respect to an external orienting field. It is found that inside the surface of the wall, the DCF rapidly tends to a function of the nematogen orientation and depends only on parameters of the bulk fluid. We suggest that the wall-nematic DCF can be used as an ansatz for the colloid-nematic DCF in dilute nematic colloids. The reliability of this ansatz is investigated at different field strengths in both isotropic and nematic regions. Our calculations for spherical colloidal particles show that this approximation is valid for colloidal particles that are large, but well within the physically realistic size range. The ansatz could also be applied to nonspherical colloidal particles.