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"I call any geometrical figure, or group of points, chiral, and say it has chirality, if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself." This definition was stated by Lord Kelvin in 1904, in his Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. The statement is universally accepted as the definition of chirality. In extremely simple words, chirality is "handedness", that is, an object or a system is different from its image and its mirror image cannot be superimposed on the original object, for example, our left and right hands.
Figure 1.1 Charility and enantiomres
In chemistry, a chiral molecule (Figure 1.1) is the one which is non-superimposable on its mirror image and it has the property (called optical activity) of rotating the polarisation plane of monochromatic light that is passed through it. Whether or not a molecule is chiral is generally determined by its symmetry. A molecule is chiral if and only if it lacks an axis of improper rotation, that is, an n-fold rotation (rotation by 360Â°/n) followed by a reflection in the plane perpendicular to this axis cannot map the molecule on to itself. A molecular and its mirror image are called "enantiomers" and different enantiomers of chiral compounds often have different taste and smell. For example, Aspartame is a sweetening agent that is more than a hundred times sweeter than sucrose. And yet, the mirror image molecule is bitter.
Chirality is closely bound up with human lives and a characteristic trait of life is its homochirality that biology uses only one enantiomer and not the other. For example, animal proteins are exclusively built from L-amino acids, while all the sugars in DNA and RNA as well as in the metabolic pathways, are R-type. The origin of this fundamental dissymmetry is still mysterious. More than that, chirality is the most important conception for modern pharmaceutical industry accounting for the quite different biological activities of the two enantiomers of drugs. In principle, stereo-selectivity of chiral drug action is derived from both pharmacodynamic and pharmacokinetic processes and can come from any and all of the processes involved in drug action, from transport to storage in depots, interaction with binding proteins or receptors, metabolic events, and terminal transport in excretory pathway . One famous example is the Thalidomide, which was used as a sedative drug from 1957 into the early 60's. The marketed drug was a 50/50 mixture. The S-isomer of thalidomide could treat the morning sickness for the pregnant women, but the R-isomer caused foetal abnormalities. Penicillamine is also a drug where D-isomer is used to treat rheumatoid arthritis while L-isomer is highly toxic. Figure 1.2 shows these two drugs that can cause different effects due to the contribution of the different isomers.
Figure 1.2 Examples of chiral drugs
Food and Drug Administration (FDA) policy published in 1992 (Chirality, 4:338-340) strongly urges companies to evaluate racemates and enantiomers for new drugs. Over the last two decades, single-ennatiomer drug sales showed a continuous growth worldwide and will continue to have a strong growth. The market for chiral drugs sold as single isomer was 22 % in 1983 and rise to 82 % in 2004 at a rate of 80 %. According to market statistics, the sales for dosage forms of single isomer drugs was 35 billion U.S. dollars in 1993, while the 1997 annual sales of about 400 to 600 billion U.S. dollars The global sales of chiral drug reached 133 billion U.S. dollars in 2002 and is expected to more than 250 billion U.S. dollars in 2010.
1.1.2 Chiral separation
Since enantiomers may exhibit different physiological activity and pharmacological effects in biological system, the synthesis and separation of enantiomers have attracted considerable attention in biological science and pharmaceutical industry [2-4].
Chiral compounds are synthesized through a sequence of chemical reactions and the chiral centers introduced at the appropriate place by incorporating chiral precursors available from the chiral pool or by employing asymmetric reactions or enantiomeric resolution process. Asymmetric reactions involve the use of chiral agents, that is, chiral auxiliaries or enantioselective catalysts, to favor the formation of the desired enantiomer. On the other hand, resolution is much more efficient than the time-consuming development of an asymmetric synthetic route which in the end will supply only one of the enantiomers. Resolution process involves the separation of two enantiomers comprising a racemic mixture and can be accomplished using a number of different techniques, including kinetic separation and physical separation. Kinetical separation relies on difference in chemical reactivity between the isomers. Enzymes are often used to catalyst the reaction that concerts on enantiomer faster or more completely than another. For example, hydrolysis of one enantiomeric ester generates an acids and an alcohol, the alcohol could be separated by ion-exchange chromatography. Physical separation bases on difference in the physical properties of the enantiomeric pairs, including crystallization, solvent extraction and chromatography and so on. Various physical separation methodologies are the most utilized techniques to analyze chiral conounds and prepare single enantiomer.
1.2 Techniques for chiral separation
Various techniques have been developed for the separation of enantiomers, such as thin-layer chromatography (TLC), high performance liquid chromatography (HPLC), gas chromatography (GC), supercritical fluid chromatography (SFC), ultra-performance liquid chromatography (UPLC), capillary electrophoresis (CE) and related electro-techniques [5-6].
For all the choromatographic techniques, the separations base on the partitioning of analytes between the stationary phase and the mobile phase. There is an associative force between the analytes and either the mobile or the stationary phase, which relies on the structure of the analytes. In chiral chromatography, the associative force arises from spatial arrangement of the analytes, and therefore, the separation lies in the selective material in the system. The choromatographic techniques (HPLC, GC, SFC UPLC) achieve enantioseparation by employing chiral stationary phase or chiral mobile phase additives in the mobile phase limited in their successful application . For the chiral recognition agent bound to the stationary phase, an increased peak broadening is expected due to the slow mass transfer. While, when the chiral selector added in the mobile phase, a large amount of selector is need especially for HPLC.
For a long time, the chiral separation is the domain of HPLC, usually employing chiral stationary phase and nonaqueous mobile phase. Although GC usually offers a higher efficiency due to a large number of plates available in the column than HPLC, the obtained diastereomers are often less volatile . This makes GC is less popular compared with the great interest in the application of chial HPLC. SFC uses supercritical fluid, usually carbon dioxide, as the mobile phase. At its critical point, the supercritical foluid shows low viscosity and high diffusivity, which is benefit to reduce analysis time and improve efficiency. UPLC is a new analysis technique developed on the basis of HPLC. UPLC is considered advantageous over HPLC due to its low mass diffusion, short analysis time, high sensitivity and efficiency.
Capillary electrophoresis (CE) is a relatively new separation technology that provides rapid analysis with high efficiency and resolution due to the use of high electric field and a variety of selective mode. By CE, the enantioseparation can be achieved by employing chiral selector in a common background electrolyte (BGE) that could be either aqueous or non-aqueous. Compared with other chromatographic techniques (HPLC, GC, SFC), the CE displays some impressive advantages as follow:
high separation efficiency. Because the absence of Eddy diffusion and mass transfer between two phases , CE offers higher plate number (N~105-106m-1) than that of HPLC (N~105m-1) and GC (N~3*103m-1) . The high efficiency of CE allows the base-line separation of enaniomers even in cases when the selectivity of dose not exceed 1.01, which is difficult in other separation techniques, such as GC ans SFC and unimaginable in HPLC .
high selectivity. The selectivity of enantioseparation in CE could exceed the thermodynamic selectivity of the chiral recognition and approaches an infinity high value, which is impossible in chromatographic techniques [9-11].
low sample and selector consumption which means low cost. Some new and expensive chiral selector could be used as usually.
low solvent consumption which is environmental friendly.
short analysis time and capability to automation.
1.3 CE for chiral separation
1.3.1 Basic concepts of CE
Modern CE appeared in the 1970s, first as isotachophoresis (ITP)  followed by capillary zone electrophoresis (CZE) . The use of CE for the enantioseparation can be date by the work of Gassmann et al in 1985 with the separation of dansyl amino acid enanitomers . According to UPAC recommendations, CE is "a separation techniques carried out in capillaries based solely on the differences in the electrophoretic mobilityies of charged species (analytes) either in aqueous or non-aqueous background electrolytes solutions. These may contain further additives, which can interact with the analytes and alter their electrophoretic mobilities" . A basic chematical of a capillary electrophoresis system is shown in Fig. 1.3.
Figure 1.3 Capillary electrophoresis system
In CE and related electro-techniques, the movement of species is controlled by the electrophoretic flow that the directional migration of charged species under electrical field and electroosmotic flow (EOF) that is generated from the mobility of the excess counter-ions attracted to the negatively charged capillary surface.
For the electrophoretic flow, cations are drawn towards cathode while anions are drawn towards anode. The neutral species do not favor either.
Figure 1.4 Electrophoretical flow
The electrophoretical mobility of a spherical solute is determined by the charge density (charge to mass ratio) as Eq. 1-1.
where q and r is the charge and the hydrated radius of the species, respectively; Î· is the viscosity of the background electrolyte.
The electroosmotical flow (EOF) is a non-selective force and push all components (charged and uncharged) migrate towards cathode.
Figure 1.5 Electroosmotical flow
A key feature of EOF is its flat flow profile which could reduce the zone broadening, leading to high separation efficiency that allow separations on the basis of mobility differences as small as 0.05 % . Contrasts with the flat flow profile of EOF in CE, the pressure-driven flow in many separation techniques (HPLC, GC, SFC) is a parabolic or laminar flow because of the pressure drop across the column caused by the friction forces at the column walls, which is led to low mass transfer and efficiency .
Figure 1.6 Electroosmotical flow and pressure-driven flow
The electroosmostical mobility depends on the zeta potential Î¶, the viscosity Î· and the dielectric constant of the background electrolyte Îµ. It can be easily measured by neutral marker, such as methanol, and it can be calculated by Eq. (1-3).
where L and l are the total and effective capillary length, respectively, V is applied voltage, t0 is the migration time of the neutral marker.
Under the control of both electrophoretical flow and electroosmotical flow, the positively charged analytes will be detected first, following by the neutral and finally the negatively charged analytes.
Figure 1.7 Migration of species in CE
The separation is achieved when analytes possess different apparent mobility difference under the applied experiment condition. The apparent mobility measured directly and calculated using the Eq. (1-4):
So, the effective mobility of analytes can be calculated using the apparent mobility miners the electroosmotic ability.
where L, l, V and t0 have the same physical meaning with those in Eq. (1-3), t is the migration time of the analytes.
1.3.2 Enantioseparation by CE
For the separation of analytes with different structures by CE, the separation depends on their different effective charge density. However, enantiomers do not differ in their charge density. Thus, enantioseparaion by CE requires the formation of diastereomers by both the indirect and direct methods.
Indirect method is based on the formation of diastereomeric complexes between the analytes and derivatization with a stereochemically pure chiral agent before the electrophoresis separation. Subsequently, the diastereomeric complexes are separated in an achiral electrophoresis system. The indirect method is straight forward from the theoretical point of view, as it is essentially an electrophoretic separation of two compounds with different mobility . However, there are some limitations of this approach. The analytes enantiomers should have a functional group that can be derivatized. The chiral derivatization agent are required to be of very high stereochemical purity and the intermolecular distance between the derivatization agent and the chiral center of the enantiomers should not be too large . Moreover, the derivatization is often a time consuming step.
The direct enantioseparation is more commonly used approach because it is more flexible and easier to operate. The direct enantioseparation is based on the formation of transient diastereomeric complexes between the analyte enantiomers and an optically pure chiral selector during the electrophoresis process. Usually, the direct enantioseparation by CE is achieved by the addition of chiral selector in the background electrolyte. This approach relays on the different intermolecular interactions between the enantiomers and the chiral selector. In the case of the formation of 1:1 complex between the enantiomers and the selector, these interactions could be described as the following thermodynamic equilibria characterized by the complxation constants.
R (S) and RC (SC) present the free enantiomer and the complex, respectively. C is the chiral selector. RC and SC The complexation constants KR and KS could be described by the following equations:
where [R], [S], and [C] are the concentration of the free enanitomers and the selector. [RC] and [SC] are the equilibrium concentration of the complexes.
Based on the primary complexation equlibria, Wren and Rowe have proposed a "mobility difference model" which expresses the enantioseparation using the apparent mobility difference of eantiomers, the maximum apparent mobility difference results in maximum separation [18-19]. According to this model, the apparent mobility difference depends on the selector concentration [C], the complexation constants KR and KS, the electrophoretical mobility of the free enantiomers Î¼f and the complexes Î¼c. The electrophoretical mobilities of the complexes RC and SC are assumed to be equal in this model.
Vigh and co-worker developed a CHARM (charged resolving agent migration) model considering not only the complexation equilibria and also the protonation (deprotonation) equilibria . In the CHARM model, the following equilibria have been considered.
Expressions are only shown for R enantiomers because both enantiomers participate in similar equlibria. Under the influence of the three equlibira, the effective charge (zReff) and effective mobility (mReff) of the R enantiomers could be described as Eq. (1-8) and Eq. (1-9), respectively.
where zi0 and mi0 are the ionic charge and mobility of the related species, K is the dissociation constant of the R enantiomer, KRC and KHRC are the complexation constant of free and protonated R enantiomer, [C] and [H3O+] are the concentration of the chiral selector and the hydronium ion in the buffer. The separation selectivity (a) is expressed as the ratio between the effective mobility of the enantiomers and used to measure the enantioseparation.
In detail, the chiral CE separation is classified to three types, depending on whether (i) only the non-ionic forms, (ii) only the ionic forms, or (iii) both forms of the two enantiomers interact selectively with the chiral selector. The determination of the effective charge (zReff), effective mobility (mReff) and selectivity (a) for the three types are summarized in Table 1.1.
Table 1.1 The effective charge (zReff), effective mobility (mReff) and selectivity (a) of chiral CE based on CHARM model
(a) in type (ii), zR0 = zS0 = z0 and mR0 = mS0 = m0.
Especially to deserve to be mentioned, although the CHARM model is developed using negatively charged single isomer CDs, it can certainly be applied to any kind of charged selectors .
1.3.3 Factors influencing the chiral CE separation
The property of the background electroplyte (BGE) is the first and most important consideration in achieving successful enantioseparation by CE.
The pH value of the BGE should be chosen carefully because it will affect both the electrophoretic mobility by changing the effective charge of the species and the electroosmotical mobility by influencing the zeta potential of the capillary [16, 22-23]. Therefore, the BGE pH could influence not only the separation selectivity but also the migration order of the enantiomers. Several publications have discussed this pH depended reversal of enantiomer migration order. Mechref and Rassi  reported the reversal of the migration order of the 1,1'-binaphthyl-2,2'-diyl hydrogen phosphate depending on the BGE pH. Sabbah and Scriba  demonstrated the effect of the BGE pH on the selectivity and migration order of dipeptide and tripeptide enantiomers. Moreover, the solubility of enantiomers and chiral selectors is also affected by the BGE pH .
The ionic strength of the BEG has significant influences on the peak shape, EOF, migration time and current. The increased ionic strength could reduce the electromigration dispersion and hence the peak tailing  at the cost of high current. The larger ionic strength also leads to lower EOF and longer migration time . To achieve optimum separation, the BGE concentration is suggested approximately 100 times greater than the injected analytes concentration and often varied in the range of 10 - 100 mM .
The type and structure of the chiral is crucial to the chiral CE because the enantioseparation relies on the formation of diastereoisomer complexes between the enantiomers and the chiral selectors. Up to now, many kinds of chiral selectors have been used, namely cyclodextrins (CDs) and their derivatives, crown ethers, marcrocyclic antibiotics, proteins, linear oligo-and polysaccharides and chiral micelles, ligand-exchange type selectors such as metal chelate complexation with copper or zinc at the centre of the complex. Different selectors have different complexes type, such as host-guest type, chelate type, affinity type (protein-ligand pairs) and, in nonaqueous system, also ion-pairing type . The concentration of the chiral selector could influences BGE viscosity, ionic strength, degree of the complexation and migration order of the analytes. Therefore, finding the optimum selector concentration is of major importance to the successful chiral CE separation.
In the enantioseparation with CDs by CE, the addition of organic modifier in BGE could affect the EOF, the viscosity and conductivity of the BGEs, the solubility of analytes and selector, as well as he dgree of complexation [19, 28-29]. It is has been observed that the organic modifier could bring about positive or negative effect on the separation depending on the type of analytes and selectors [30-33].
The capillary temperature is a key parameter to be controlled in chiral CE because it affects the electrophretical mobility of the analytes, the equilria of the complexation, etc . Several publications about the influences of temperature on the enantioseparation have been reported and generally found a reduction of either migration time or resolution on increasing the temperature [35-36]. The opposite trend was also noticed [37-38].
In addition, the applied voltage, capillary condition, and other additives in the BGEs are also important factors to be control in improving the CE enantioseparation.
1.4 Chiral separation by cyclodextrins (CDs) and its derivatives
1.4.1. CDs and its chiral recognition ability
Cyclodextrins (CDs) are cyclic oligosaccharides composed of D(+)-glucopyranose units bonded through Î±-(1,4) linkage, their shape is similar to that of a truncated cylinder with an hydrophobic cavity and an hydrophilic outside region due to the secondary C2- and C3- hydroxyl groups located on wild rim and the primary C6- hydroxyl group occupied the narrow rim (Fig. 1.8).
Figure 1.8 Structure of cyclodextrins
Figure 1.9 Inclusion complexes between CDs and guest molecule
CDs formed from 6-12 glucose units have been isolated, only those with six, seven and eight units are currently used, called Î±-, Î²-, and Î³-CDs respectively, which possess the same depth but different width. As shown in Figure 1.9, CDs could form inclusion complexation with a great variety of molecules having the size of one or two benzene rings, or even larger compounds, which have a side chain of comparable size . Inclusion complex formation between CDs and guest molecule is stereoselective, thus it affords the ability of resolving enantiomers which was first discovered by Gramer in the 1950s . In the 1980's, Armstrong established a model for the chiral discrimination by CDs . It is postulated that (i) there should be a steric compatibility between the CDs cavity and the guest molecule so that the guest molecule could be included or partially included in the CDs cavity; (ii) the affinity of the guest molecule for the CDs cavity should be higher than that for other species (i.e. solvent moleculde) and the fit of the guest into the annulus should be tight. It has been proven that, besides the besides steric compatibility, hydrophobic interaction , hydrogen bonding , electrostatic interaction , and van der waals interaction forces  could also play a considerable role in the chiral discrimination.
Due to their strong resolving ability, UV transparency and relatively low price, CDs have been widely used in pharmaceutical, food, and cosmetic industry is also important for their analytical applications. By far CDs are the most popular chiral selectors in various separation techniques, such as GC, HPLC, SFC, CE, CEC and so on.
1.4.2 Chiral separation by CE with CDs and derivatives
184.108.40.206 Neutral CDs derivatives for chiral CE separaion
Snopek and co-worker firstly applied CDs in capillary isotachophoresis (ITP) , and then the first application of CDs as chiral selector for the enanatioseparation by CE was reported by Guttman . Since then, a plenty of papers have been published on native CDs and its application in enantioseparation by CE. To enhance the chiral discrimination ability and alert other properties (such as cavity size, aqueous solubility, etc) of native CDs, the native CDs are chemically modified to generate numerous CDs derivatives. The most straightforward way to elaborate native CDs is through modification of their hydroxyl groups . Because there are numerous primary and secondary hydroxyl groups on the CDs, the modification of the hydroxyl groups usually occur in a random fashion and resulted in CDs derivatives as randomly substituted mixture which bring about the reproducibility and efficiency problems. Therefore, selectively substituted and single isomer CDs are developed to afford good reproducibility and resolution. Some commercially neutral CDs derivatives have been listed in Table 1.2.
Table 1.2 Commercial native CDs and their neutral derivatives
randomly substituted (CH3)
randomly substituted (CH3)
randomly substituted (CH2CH2CH2OH)
randomly substituted (CH2CH2CH2OH)
randomly substituted (CH2CH2CH2OH)
substituted (CH3) in position 2 and 6
substituted (CH3) in position 2, 3 and 6
220.127.116.11 Charged CDs derivatives for chiral CE separaion
Besides the neutral CDs derivatives, the synthesis and application of charged CDs derivatives become a recent trend. Compared with native CDs, the charged CDs are advantageous not only in high water solubility but also in effective separation of oppositely charged analytes by their strong electrostatic attraction in addition to the effects of inclusion complexation . High enantioselectivity and resolution can be achieved at very low concentration of charged CDs because the charged CDs could provide a self-mobility .The charged CDs could be also used as a carrier of neutral enantiomers and the EOF is not necessary in this case . Further more, the application of the charged CDs offer the easy adjustment of the enantiomer migration order .
Since the first report about the enantioseparation by CE used the charged CDs in 1989 [49, several interesting papers have been published focus on the application of charged CDs for the chiral CE. Some charged CDs have been commercial available (Table 1.3).
Table 1.3 Commercial charged CDs derivatives
Sulfated a-cyclodextrin (S-a-CD)
randomly substituted (SO3Na)
Sulfated b-cyclodextrin (S-b-CD)
randomly substituted (SO3Na)
Sulfated g-cyclodextrin (S-g-CD)
randomly substituted (SO3Na)
randomly substituted (CH2COONa)
substituted (SO3Na) in position 6
Substituted (CH3CO) in position 2 and 3, (SO3Na) in position 6
As shown in Table 1.3, most of the commercial charged CDs are randomly substituted. The substitution distribution strongly influences the selectivity, resolution, reproducibility and the efficiency of the chiral separation process. So, single-isomer charged CDs are required, that is just one position of CD rim is substituted by charged group. The single-isomer CDs offer good reproducibility and resolution and produce low Joule-heating which is favorable to high efficiency.
Vigh's group first reported the synthesis of three negatively charged single isomer CDs, namely, heptakis-6-O-sulpho-b-cyclodextrin (HS-b-CD) , Heptakis-(2,3-di-O-acetyl- 6-O-sulpho)-b-cyclodextrin (HDAS-b-CD)  and Heptakis-(2,3-di-O-methyl-6-O-sulpho) -b-cyclodextrin (HDMS-b-CD) . Afterwards, they described the synthesis and application of a series of negatively charged single isomer CDs to a broad spectum of neutral, basic, acidic and zwitterionic enantiomers [53-60]. Numerous works have reported the use of anionic single-isomer CDs, as indicated in several reviews [34, 61-63], while there are much less reports on the application of cationic single-isomer CDs. Most of the reported positively charged single isomer CDs are amino functionalized, such as 6-dimethylamino-b-CD , 6-methylamino-b-CD , 6-amino-b-CD , 2-hydroxyl-3-triethylaminopropyl-b-CD , heptakis(6-methoxyethylamino)-b-CD , 6-N-histamino-b-CD , hydroxyalkylamino-b-CD , 6-O-(2-hydroxy-3-trimethylammoniopropyl)-b-CD , 6-[1-(2-amino)ethylamino)]-b-CD , and 6-N,N,Nâ€²,Nâ€²,Nâ€²,-pentamethylethylenediammonio-b-CD . Our group have introduced a family of single-isomer positively charged CDs, mono-alkylimidazolium-Î²-cyclodextrin derivatives . These single-isomer charged CDs showed powerful resolution ability to hydroxyl acids, carboxylic acids, and useful to dansyl amino acids [74-75]. The latesd development on the application of charged CDs for the enantioseparation has be reviwed in revent publications [48, 76].
1.5 UPLC for enantioseparation separation
As mentioned above, many efforts have been dedicated to rapid chiral discrimination technology as it is crucial in pharmaceutical industry . In recent years, ultra high pressure liquid chromatography (UHPLC) technique, which employs sub-2-micron silica particles and much shorter columns than traditional HPLC , exhibits good sample capability, high efficiency, rapid analysis and requires less organic solvents. With improved hardware technology and new development of novel column packing materials, the problem of high back-pressure has been overcome and more analysis has been realized with this technique. Ultra high pressure LC has great potential in providing a platform to investigate the chromatographic performance involving the use of costly chiral additives. The first commercial UPLC system (Acquity UPLC system) was developed by Waters in 2004, which could withstand pressure up to 1000 bar. Very recently, Aglient commercialized its 1290 infinity RRLC system which is tolerant to a pressure of 1200 bar. Ultra high pressure LC technique can serve as an analytical tool for rapid-throughput analysis. Determination of doxazosine in human plasma was done by Al-Dirbashi et al by UPLC/MS . Apollonio et al communicated the UPLC/MS determination of amphetamine and ketamine substances for forensic and toxicological analysis . SpáÄil et al reported the analysis of phenolic compounds in HPLC and UPLC . A method based on UPLC/MS determination of thyreostatic drugs was reported by Abuín et al . Determination of diastereomers of SCH 503034 in monkey plasma and lacidipine in human plasma were carried out by Wang et al  and Tang et al  with UPLC/MS system, respectively. Very few works report the application of high pressure LC on enantioseparation. In one work by Guillarme et al, three amphetamine derivatives were partially separated by employing hydroxypropyl b-CD (HP-b-CD) as the mobile phase additive .
1.6 Study of cycodextrins using computational chemistry
1.6.1 Molecular modeling
As a branch of theoretical chemistry, Computational chemistry initially began with the development of quantum mechanics in the 1920's and had been improved tremendously along with the revolutionary advances in computing techniques over the last two decades . Computational chemistry has a broad range of applications from molecular modeling to the simulation and control of chemical process. It can be used to predict the characteristics and behavior of a chemical system provide useful information about orbital energy and shape of molecule, it is more widely accepted to complement, guide experimental measurement.
One of important aspect of computational chemistry is "molecular modeling", which involves the molecular simulation at atomic level. Compared to macroscopic model, which described characteristics of a whole system or process without considering the features of individual molecules, the "molecular modeling " is a microscopic, atomistic modeling using theory from first principles . There are many tools for molecular modeling, such as quantum mechanics (QM), molecular mechanics (MM), molecular dynamics (MD), Monte Carlo simulations (MC), and so on. MM uses Newtonian mechanics to model molecular systems. MD, which bases on statistical mechanics, allows atoms and molecules to interact for a period of time by approximations of known physics, giving a view of the motion of the particles. MC uses statistical mechanicals to provide average energy and property of system depending on repeated random sampling. The potential energy of all atoms is calculated using force fields in MM, MD and MC. Contrasted to MM, MD and MC used an empirical force field (EFF), the QM commonly employ the molecular orbital theory (MOT) to locate all electrons and nuclei to obtain a lowest energy state of the entire system . The structure and electronic features of molecules could be predicted after the energy minimization (also called geometry optimization).
The QM methods include ab initio methods, semi-empirical methods and denstity functional quantum mechanics methods. As compared to the all-electron methods of ab initio and DFT quantum mechanical calculation, the semi-empirical quantum mechanical method is valence-electron only methods . The ab initio and DFT methods expand molecular orbital into a linear combination of atomic orbitals and do not immediately introduce any further approximation. Ab initio use Hartree-Fock calculations to get the final wave function and determine the system energy while DFT calculations approximate the relationship of the energy to the electron density. Semi-empirical quantum chemistry methods are based on the Hartree-Fock formalism, but make many approximations and obtain some parameters from empirical data. Semi-empirical quantum mechanics methods have evolved over the last three decades. Using today's microcomputers, they can produce meaningful, often quantitative, results for large molecular systems.
The semi-empirical methods have several advantages over ab initio and density functional methods. Most importantly, these methods are fast, the time scale for most semi-empirical methods is n3, while about n4 for the ab initio methods, where n is the number of mathematical functions needed to describe each atomic orbital . The high computational efficiency permits the modeling of large system beyond the capacity of ab initio methods with comparable precision to that of ab initio methods with medium sized basis set [89-91]. Therefore, the semi-empirical methods are very important in computational chemistry for treating large molecules where the full Hartree-Fock method without the approximations is too expensive. Another advantage is that for specific and well-parameterized molecular systems, these methods can calculate values that are closer to experiment than lower level ab initio and density functional techniques .
1.6.2 Computational studies of cycodextrins
The hydrophobic cavity with appropriate dimensions of b-CDs enables them to form inclusion complexes with various compounds by admitting inside the cavity of guest molecules without covalent bonds. This property has been exploited to the biochemistry, pharmaceutical industry and many areas of chemistry. Theoretical investigation of the CDs inclusion complexes using molecular modeling could provide significant insight into the non-covalent intermolecular interactions. However, the relative large size of CDs and their derivatives limited the modeling study, because many assumptions and restrictions have to be imposed which makes the computation is too expensive . In addition, CDs are usually investigated experimentally in aqueous media, which is hard to deal with in computational chemistry . Therefore, most studies of CDs complexes based on molecular mechanicals (MM) , molecular dynamics (MD)  and Monte Carlo simuations (MC) . Last two decades, the rapid development of computer technology make the quantum mechanical (QM) computation of CDs could be carried out in a reasonable time period. Since the first quantum mechanical (QM) study of CDs using semi-empirical CNDO method performed by Kitagawa et al in 1987 , many QM computations have been carried out using the most advanced semi-empirical methods, such as AM1, MM2, PM3 and so on, to investigate the structure of the CDs complexes as well as the driving force of the complexation process. The semi-empirical methods could reduced even avoid the structure restriction and the symmetry constraints necessary for the MM and MD calculation .
1.7 Research objectives and scope
Five pyrrolidinium substituted cationic b--CD chiral selectors were synthesized and their chiral discrimination ability was evaluated and compared by CE and UHPLC using a broad spectrum of acidic enantiomers.
Our group have previously reported a series of single-isomer, b-CDs bearing imidazolium substituents on the C6 position, which displayed good chiral discrimination of dansyl amino acids [73-75]. However, the strong UV absorption by the imidazolium moiety interfered with analyte detection. In addition, there are very limited publication about the saturated heterocyclic group modified single-isomer cationic CDs. Herein, to avoid the detection problem and enlarge the range of the positively charged single isomer CDs, a family of well-designed single isomer cationic CDs were synthesized in this thesis by introducing different non-planer pyrrolidinium group on C6 of b-CDs.
These cationic single isomer CDs were employed as chiral selector in CE for the chiral separaation of various enantiomers. The parameters that could effect the enantioseparation, such as background electrolyte pH, selector concentration, organic modifier, applied temperature, were investigated and the optimum operation condition was found.
The chiral resolving ability of these cationic single isomer CDs was compared using a series of anionic and ampholytic acids investigate the effect of the different pyrrolidine substituents with various alky group. The complexation stability constants of between CDs and model enantiomers were determined to support the experiment results.
The chiral resolving ability of these structurally well defined single isomer cationic pyrrolidinium CDs were further tested and compared using UHPLC. They were used as mobile phase additivesmobile phase additives in enantioseparation of a series of dansyl amino acid an Agilent C18 column. The influence of selectors and organic modifier proportions on the enantioseparation was studied in detail to achieve the optimum separation.
In addition, the molecular modeling was carried out to provide more insight into the structure of the host-guest CD complexe and the help to illustrate the chiral discrimination process.