The hydrogen molecule for a two-dimensional system

The two-dimensional (2D) energy of the hydrogen molecule is carried out by the Heitler-London method. The 2D integrals (which are more localized compared to 3D ones) are performed in the light of the 3D Slater integrals. A discussion of such 2D systems is briefly outlined for doped semiconductors.     

Analysis of two-dimensional models for liquid chromatographic reactors of cylindrical geometry

This work presents the analytical solutions of two-dimensional isothermal reactive general rate models for liquid chromatographic reactors of cylindrical geometry. Both irreversible and reversible reactions are considered. The model equations form a linear system of convection-diffusion-reaction partial differential equations coupled with algebraic equations for isotherms. Analytical solutions are derived by integrated implementation of finite Hankel transform, Laplace transform, eigen-decomposition technique, and conventional ordinary differential equations solution technique. To verify the analytical results, a high-resolution finite volume scheme is also applied to numerically approximate the model equations. The current results can be very useful to optimize and upgrade the liquid chromatographic reactors.     

Phase cycling schemes for two-dimensional optical spectroscopy with a pump–probe beam geometry

We present phase cycling schemes for two-dimensional (2D) optical spectroscopy with a pump–probe beam geometry. We detail the theoretical derivation on how the phase cycling schemes measure a pure absorptive 2D spectrum. The ‘rotating frame’ is inherent in such phase locked phase cycling experiments, and can increase the efficiency of the experiment by reducing the number of data points needed to be collected. 2D optical spectra are simulated for the phase cycling pump–probe experiment by solving the Liouville equation that describes the system-field interaction using a non-perturbative method.     

Formation of capillary bridges in two-dimensional atomic force microscope-like geometry

We discuss the phase diagram of a fluid confined in a two-dimensional atomic force microscope-like geometry which allows the formation of liquid bridges connecting the opposite walls. The corresponding phase behavior of the fluid is influenced by the phenomenon of complete filling of a wedge.     

Effect of particle geometry on phase transitions in two-dimensional liquid crystals

Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles. We find profound differences in the phase behavior of these models, which can be attributed to their different packing properties. Interestingly, bimodal orientational distribution functions are found in the nematic phase of hard rectangles, which cause a certain degree of biaxial order, albeit metastable with respect to spatially ordered phases. This feature is absent in discorectangles, which always show unimodal behavior. This result may be relevant in the light of recent experimental results which have confirmed the existence of biaxial phases. We expect that some perturbation of the particle shapes (either a certain degree of polydispersity or even bimodal dispersity in the aspect ratios) may actually destabilize spatially ordered phases thereby stabilizing the biaxial phase.     

Phase diagram of a two-dimensional system with anomalous liquid properties

Using Monte Carlo simulation techniques, we calculate the phase diagram for a square-shoulder square-well potential in two dimensions that has been previously shown to exhibit liquid anomalies consistent with a metastable liquid-liquid critical point. We consider the liquid, gas, and five crystal phases, and find that all the melting lines are first order, despite a small range of metastability. One melting line exhibits a temperature maximum, as well as a pressure maximum that implies inverse melting over a small range in pressure.     

Optimization of a comprehensive two-dimensional normal-phase and reversed-phase liquid chromatography system

The present investigation is based on the evaluation of the performance of a comprehensive two-dimensional liquid chromatography (LCxLC) system during method optimization. The LCxLC set-up, operated in normal phase (NP) mode (adsorption) in the first dimension (1D) and reversed-phase (RP) mode in the second dimension (2D), is equipped with a 1D microbore silica column and a 2D monolithic C(18) column with a 10-port two position valve as the interface. A photodiode array detector is used after the 2D separation. A possible cause of peak distorsion because of the immiscibility of the mobile phases employed in the two dimensions is resolved. The optimization of the analytical run time and flow rate for both dimensions and the initial gradient in the 2D is carried out with various standard compounds. The potential and versatility of this LCxLC approach is demonstrated through the separation of 11 standard components, most of them allergens. The latter, which are characterized by a scattered distribution on the 2D space plane, underwent separation on both a hydrophobicity and polarity basis.     

Molecular geometry and symmetry from a differential geometry viewpoint

Relations between an earlier generalization of molecular symmetry called symmorphy and a molecular equivalence based on diffeomorphisms of electron density functional graphs (the so-called DFG equivalence introduced in our previous work) are analyzed. Any two DFG-equivalent electron density functions can be derived from one another by a suitable transformation of the spatial coordinates and the electronic charge density scale; the classes of DFG equivalence are the orbits of a group of linear operators operating in the space of electron density functions. Within the symmorphy framework, the symmetry group is derived from the symmorphy group by taking an intersection of a subgroup of the symmorphy group and the group of isometries for a natural choice of the Riemannian metric tensor. The Riemannian metric properties provide a choice for a suitable reference electron density function for each class of equivalent densities. Such reference densities serve as tools for a systematic classification of the infinite family of electron densities of molecular conformations. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 669–678, 1997     

去除血浆中高丰度蛋白质的二维液相色谱体系的建立

血浆中高丰度蛋白质的存在严重干扰低丰度蛋白质的检测,是困扰血浆蛋白质组学研究的技术瓶颈之一。针对这一热点问题,建立了一种二维液相色谱(强阴离子交换色谱-反相高效液相色谱)分离系统,对血浆中的高丰度蛋白质进行了色谱定位并进行去除。选择TSKgel SuperQ-5PW为第一维色谱分离柱,第二维色谱分离采用Jupiter C4柱,对第一维的馏分进行进一步的分离。通过梯度优化,血浆样品经过二维系统得到充分分离。第二维分离过程中从紫外信号强度高(215 nm,大于20 mAU)的峰中选择10个峰,利用液相色谱-串联质谱鉴定出32种高丰度蛋白质,包括人血清白蛋白、免疫球蛋白G等高丰度蛋白质。该体系为血浆中更多高丰度蛋白质的去除以及血浆蛋白质组学的更深入研究提供了重要思路。     

Elucidation of a low spin cobalt(II) system in a distorted tetrahedral geometry

We have prepared a series of divalent cobalt(II) complexes supported by the [PhBP(3)] ligand ([PhBP(3)] = [PhB(CH(2)PPh(2))(3)](-)) to probe certain structural and electronic phenomena that arise from this strong field, anionic tris(phosphine) donor ligand. The solid-state structure of the complex [PhBP(3)]CoI (1), accompanied by SQUID, EPR, and optical data, indicates that it is a pseudotetrahedral cobalt(II) species with a doublet ground state-the first of its type. To our knowledge, all previous examples of 4-coordinate cobalt(II) complexes with doublet ground states have adopted square planar structure types. Complex 1 provided a useful precursor to the corresponding bromide and chloride complexes, ([PhBP(3)]Co(mu-Br))(2), (2), and ([PhBP(3)]Co(mu-Cl))(2), (3). These complexes were similarly characterized and shown to be dimeric in the solid-state. In solution, however, the monomeric low spin form of 2 and 3 dominates at 25 degrees C. There is spectroscopic evidence for a temperature-dependent monomer/dimer equilibrium in solution for complex 3. Furthermore, the dimers 2 and 3 did not display appreciable antiferromagnetic coupling that is typical of halide and oxo-bridged copper(II) and cobalt(II) dimers. Rather, the EPR and SQUID data for solid samples of 2 and 3 suggest that they have triplet ground states. Complexes 1, 2, and 3 are extremely oxygen sensitive. Thus, stoichiometric oxidation of 1 by dioxygen produced the 4-coordinate, high spin complex [PhB(CH(2)P(O)Ph(2))(2)(CH(2)PPh(2))]CoI, (4), in which the [PhBP(3)] ligand had undergone a 4-electron oxidation. Reaction of 1 with TlOAr (Ar = 2,6-Me(2)Ph) afforded an example of a 4-coordinate, high spin complex, [PhBP(3)]Co(O-2,6-Me(2)Ph) (5), with an intact [PhBP(3)] ligand. The latter two complexes were spectroscopically and structurally characterized for comparison to complexes 1, 2, and 3. Our data for these complexes collectively suggest that the [PhBP(3)] ligand provides an unusually strong ligand-field to these divalent cobalt complexes that is chemically distinct from typical tris(phosphine) donor ligand sets, and distinct from tridentate borato ligands that have been previously studied. Coupling this strong ligand-field with a pronounced axial distortion away from tetrahedral symmetry, a geometric consequence that is enforced by the [PhBP(3)] ligand, provides access to monomeric [PhBP(3)]CoX complexes with doublet rather than quartet ground states.     

Development of a switchable multidimensional/comprehensive two-dimensional gas chromatographic analytical system

In this study, a new system for analysis using a dual comprehensive two-dimensional gas chromatography/targeted multidimensional gas chromatography (switchable GC × GC/targeted MDGC) analysis was developed. The configuration of this system not only permits the independent operation of GC, GC × GC and targeted MDGC analyses in separate analyses, but also allows the mode to be switched from GC × GC to targeted MDGC any number of times through a single analysis. By incorporating a Deans switch microfluidics transfer module prior to a cryotrapping device, the flow stream from the first dimension column can be directed to either one of two second dimension columns in a classical heart-cutting operation. Both second columns pass through the cryotrap to allow solute bands to be focused and then rapidly remobilized to the respective second columns. A short second column enables GC × GC operation, whilst a longer column is used for targeted MDGC. Validation of the system was performed using a standard mixture of compounds relevant to essential oil analysis, and then using compounds present at different abundances in lavender essential oil. Reproducibility of retention times and peak area responses demonstrated that there was negligible variation in the system over the course of multiple heart-cuts, and proved the reliable operation of the system. An application of the system to lavender oil, as a more complex sample, was carried out to affirm system feasibility, and demonstrate the ability of the system to target multiple components in the oil. The system was proposed to be useful for study of aroma-impact compounds where GC × GC can be incorporated with MDGC to permit precise identification of aroma-active compounds, where heart-cut multidimensional GC-olfactometry detection (MDGC-O) is a more appropriate technology for odour assessment.     

Development of a new fluorescence decay measurement system using two-dimensional single-photon counting

A new fluorescence decay measurement system has been developed. The system consists of a spectrograph and a new two-dimensional photon counter. The combination enables measurements to be made of the fluorescence decay as a function of time and wavelength simultaneously. The time resolution is better than 5 ps with deconvolution processing, and the wavelength resolution is approximately 0.15 nm with 1200 grooves mm⁻¹ gratings. The dynamic range is 10⁵. The instrument response function (IRF) of the system is nearly gaussian, and has no tail or “after pulses” which are commonly observed using a photomultiplier in a time-correlated photon counting (TCPC) system. Therefore fast fluorescence decay of several tens of picoseconds can be measured accurately. In addition, the two-dimensional single-photon counting can be performed without wavelength scanning, so that the wavelength-dependent fluorescence decay can be easily and direcly observed with a fast throughput and a high signal-to-noise ratio. The principle of two-dimensional photon counting is discussed together with characteristics including linearity and statistical behavior.     

Homo- and heteronuclear two-dimensional covariance solid-state NMR spectroscopy with a dual-receiver system

Two-dimensional (2D) covariance NMR spectroscopy, which has originally been established to extract homonuclear correlations (HOMCOR), is extended to include heteronuclear correlations (HETCOR). In a (13)C/(15)N 2D chemical shift correlation experiment, (13)C and (15)N signals of a polycrystalline sample of (13)C, (15)N-labeled amino acid are acquired simultaneously using a dual-receiver NMR system. The data sets are rearranged for the covariance data processing, and the (13)C-(15)N heteronuclear correlations are obtained together with the (13)C-(13)C and (15)N-(15)N homonuclear correlations. The present approach retains the favorable feature of the original covariance HOMCOR that the spectral resolution along the indirect dimension is given by that of the detection dimension. As a result, much fewer amounts of data are required to obtain a well-resolved 2D spectrum compared to the case of the conventional 2D Fourier-Transformation (FT) scheme. Hence, one can significantly save the experimental time, or enhance the sensitivity by increasing the number of signal averaging within a given measurement time.     

The energy levels for a symmetric and nonsymmetric double-well potential in a two-dimensional system using the Hill determinant approach

Energy levels of the Schrödinger equation for a double-well potentialV(x, y; Z _x ², Z_y ²,) = –Z _x ² x ² -Z _y ² y ² +[a _xx x ⁴ + 2a _xy ^x 2y2 +a _yy y ⁴] in a two-dimensional system are calculated using the Hill determinant approach for several eigenstates and over a wide range of values of the perturbation parameters (, Z _x ²,Z _y ²). Some of the results calculated by the Hill determinant approach are compared with those results produced by the inner product technique.     

On-line coupling of capillary isoelectric focusing with transient isotachophoresis-zone electrophoresis: a two-dimensional separation system for proteomics

A microdialysis junction is employed as the interface for on-line coupling of capillary isoelectric focusing with transient isotachophoresis-zone electrophoresis in a two-dimensional separation system. Capillary isoelectric focusing not only provides high-resolution separation of tryptic peptides based on their differences in isoelectric point, but also potentially allows the analysis of low-abundance proteins with a typical concentration factor of 50-100 times. Carrier ampholytes, employed for the creation of a pH gradient during focusing, are further utilized as the leading electrolyte in the second separation dimension, transient isotachophoresis-zone electrophoresis. Many peptides which have the same isoelectric point would most likely have different charge-to-mass ratios, and thus different electrophoretic mobilities in zone electrophoresis. Two-dimensional separation of proteolytic peptides is demonstrated using standard proteins, including cytochrome c, ribonuclease A, and carbonic anhydrase II. The maximum peak capacity is estimated to be around approximately 1600 and can be significantly increased by simply increasing the capillary column length and manipulating the range of pH gradient in isoelectric focusing. In addition to enhanced separation efficiency and resolution, this two-dimensional electrokinetic separation system permits sensitive and comprehensive analysis of peptide fragments, especially when integrated with electrospray ionization mass spectrometry for peptide/protein identification.     

基于集成化多柱二维液相色谱系统分析血清中的氨磺必利

快速准确的治疗药物监测对于临床上确保患者用药有效性及安全性至关重要,同时也能够确定患者用药依从性,制定个性化给药方案。该文以两支疏水性略有差异的反相分离柱Supersil ODS2和SinoChrom ODS-BP,及强阳离子交换捕集柱Supersil SCX构建了基于集成化的多柱二维液相色谱系统。通过二维色谱接口,以pH 3.0的磷酸缓冲液调整第一维分离后的洗脱液组成,降低有机相含量并维持pH,改善了中心切割模式下样品转移和捕集的效率。利用该多柱二维液相色谱系统发展了血清中氨磺必利的二维液相色谱检测方法,血清样品经过高氯酸和甲醇混合液沉淀蛋白质并离心后直接300 μL大体积进样,以乙腈/磷酸缓冲液(25 mmol/L, pH 3.0)(20/80, v/v)作为第一维分离流动相,磷酸缓冲液(25 mmol/L, pH 3.0)作为捕集过程的稀释流动相,乙腈/磷酸缓冲液(25 mmol/L, pH 7.0)(25/75, v/v)作为第二维分离流动相,12 min内即可完成分析。方法在10~200 ng/mL的范围内线性相关性良好(r=0.9998)。样品在50 ng/mL和100 ng/mL两个加标浓度下的回收率稳定,在73.7%~76.8%之间。方法的检出限为7.28 ng/mL,定量限为24.27 ng/mL,能够满足《神经精神药理学治疗药物检测共识指南》中推荐的药物监控范围要求。由于该系统日常使用及维护成本较低,且能够实现自动化分析,故该方法适合在临床上用于治疗药物监测研究。