Electron Momentum Spectroscopy and Its ...

Electron Momentum Spectroscopy and Its Applications to Molecules of Biological Interest Feng Wang Centre for Molecular Simulation, Swinburne University of Technology, P. O. Box 218, Hawthorn, Melbourne, Victoria, 3122, Australia Abstract. Energy and wave function are the heart and soul of Schrodinger quantum mechanics. Electron momentum spectroscopy (EMS) so far provides the most stringent test for quantum mechanical models (theory, basis sets and the combination of both) through observables such as binding energy spectra and Dyson orbital momentum distributions. The capability of EMS to measure Dyson orbitals of a molecule as momentum distributions provides a unique opportunity to assess the models of quantum mechanics based on orbitals, rather than on energy dominated (mostly isotropic) properties. Recently, the author introduced a technique called dual space analysis (DSA), which is based on EMS and quantum mechanics to analyze orbital based information in the more familiar position space as well as the less familiar momentum space. In this article, the development of EMS and DSA is reviewed through the applications to molecules of biological interest such as amino acids, nucleic acid bases and recently nucleosides. The emphasis is the applications of DSA to study isomerization processes and chemical bonding mechanisms of these molecules. Keywords: Electron momentum spectroscopy, density functional theory calculations, binding energy spectra, orbital momentum distributions, dual space analysis, atoms in molecules, conformers and tautomers.

PACS:31.15.Fx, 31.25.Qmand36.20Kd

INTRODUCTION Structure dictates function. N o w h e r e is this more apparent than in biological systems (Pratt, 2006). Noble Laureate Francis Crick indicated: "if y o u wish to k n o w function, study shape." This is particularly true in the study of biological systems, such as genetic materials, proteins and enzymes. M a n y biological p h e n o m e n a can be traced back to fundamental properties of molecular components. For example, the base of the famous Watson-Crick D N A structure discovery (Watson & Crick, 1953) is the insight into the structure of genetic material, e.g., D N A , at molecular level. Shape (structure) determines whether the atoms that can form bonds to the atoms of another molecule are in close proximity of each other. Properties of related fragments and molecules, such as D N A / R N A fragments

CP963, Vol. 1, Computational Methods in Science and Engineering, Theory and Computation: Old Problems and New Challenges, edited by G. Maroulis and T. Simos © 2007 American Institute of Physics 978-0-7354-0477-9/07/$23.00

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and amino acids, are fundamental to the understanding of complex structures such as proteins, drug discovery and even in novel electronic and optoelectronic devices based on or modified by molecular species. Electronic structure is central for the properties of a system built up of atoms, such as molecules, liquids and solids. A fundamental understanding of the electronic structure in small molecules and fragments is crucial for the understanding of many-atom systems, such as drugs and proteins. It is also the microscopic origin of such macroscopic properties as well as chemical bonding mechanisms and to certain extent, chemical reactions. Three-dimensional (3D) geometries primarily determine the shape of bio-molecular systems but do not explicitly provide information about distributions of the electrons and it is the distributions of electrons which are responsible for chemical structures, properties and reactions (Wang, 2007a). For example, adenine and unsubstituted purine (Saha et al, 2007b) have almost the same purine ring with nearly identical purine ring perimeter, RT^

Pi

O

c-c J

0 -

II

. N — H '

III

1.908 A

0.56 kcal-mol-> c-c, C-N, C-O

IV

Glycine Conformers Fig. 5 Relative energy of four glycine Cs conformers (Falzon and Wang, 2005).

The calculated binding energy (ionization energy) spectrum of glycine (Falzon and Wang, 2005) using various quantum mechanical models compares favorably with the observed using PES (EClasinc, 1976) and EMS (Neville et al, 1996), as indicated in Table 1 (Falzon and Wang, 2005). Fingerprint (signature) orbitals of a conformer (or rotation of a single bond) with respect to a reference configuration, usually the global minimum configuration, are defined as orbitals with the most significant changes in the orbital MDs (Wang and Downton, 2004). For conformers containing a a^ (molecular) plane, the most significant variation in conformation is dominated by a' orbitals, this is also seen in other molecules such as adenine (Saha et al, 2006; Saha et al, 2007) and guanine (Jones et al, 2006). The signature orbitals lie in the molecular plane which is dominated by a-bonds. Table 1 Six outer most valence ionization energies (eV) of glycine calculated using the RHF, DFT-SAOP and OVGF models, together with available experimental results and a previous P3 model for conformer I. OVGF/TZVP Orbital

SAOP/ATZP'

RHF/TZVP P3/6-311G** "

Expt"

(pole strength) 16a' (HOMO)

10.4(10.5)

10.0(0.93)

11.3

9.9

10 (-10)"

15a'

11.4(11.5)

11.4(0.91)

12.8

11.0

11.1 (-11.2)"

4a"

12.7(12.7)

12.4(0.91)

13.4

12.2

12.1 (-12.2)"

3a"

13.5(13.6)

13.6(0.90)

14.6

13.5

13.6 (-13.5)"

14a'

14.3 (14.4)

14.8 (0.92)

16.0

14.6

14.4 (-14.2)"

13a'

15.0(15.0)

15.1 (0.92)

16.5

14.8

15.0 (-15.0)"

i Values based on the DFT-SAOP/TZ2P method are given in parenthesis. ii P3/6-311G** model (Herrera, 2004). iii Photoelectron Spectroscopy using He I (584 A) and He II (304 A) radiation lines (Debies and Rabalais, 1974). iv He I Photoelectron Spectroscopy (Klasinc, 1976).

67

HOMO (16a')

NHOMO(15a')

5.0x10"

«

— I

- - n

«

IV .0x10"*-

^W 0.010

20

30

3a' 5.0x10 1

2.5x10 •

13a' 1.6x10"

8.0x10"

Azimuthal A i ^ e (p/^ Fig.6 Orbital momentum distributions of the six outermost valence orbitals of the four glycine Cs conformers.

In Fig. 6 the orbital MDs of six outer most orbitals of the four Cj glycine conformers are presented. No all of the outer most valence orbitals are affected by the rotations of related single bond of glycine. It is seen that two orbitals, 4 a " and 3a", which exhibit Ti-bonding nature as shown in the orbital electron density distributions in the middle (4a"), do not change significantly in orbital MDs. However, almost all orbitals with a' symmetry, including the HOMO (16a'), next HOMO (15a'), 14a' and 13 a' demonstrate conformer related changes. As a result, the orbital MDs are very sensitive to the in-plane a-bonding of the Cj glycine conformers, whereas the out of plane Ti-bonds remain little affected. 4. Orbital Signatures for Adenine Tautomers (Base) The lone-pair electrons of nitrogen atoms in DNA (RNA) bases lead to a number of tautomers of comparable energies in the electronic ground states. Vital for understanding chemical reactivity, tautomerization is widely believed to lead to various biochemical processes including point mutation (Harris et al, 2003). Hence, even the minor tautomers should not be ignored (Harris et a l , 2003). The existence of adenine tautomers is confirmed by experimental studies (Gu and Leszczynski, 1999; Luhrs et. a l , 2001), often in the presence of metal (Vrkic et a l , 2004). For example, existence of tautomeric forms of adenine in a complex with transition metal ions is also revealed (Rubina and Rubin, 2005). Although many DNA (RNA) tautomers can be observed using jet-cooled spectroscopy such as resonance two-photon ionization (R2PI), the mobility of certain hydrogen atoms has brought considerable difficulties to experiment (Sobolewski et a 1., 2002), in which the signal assignment has largely relied on theoretical calculations (Lee et al., 2002; Lee et a l , 2003). Adenine could form as many as 14 different tautomers considering the different positions of the protons (Hanus et a l , 2004; Fonseca Guerra et al, 2006). Adenine prototropic tautomers can be produced by transferring the mobile proton on N(9) position (canonical form (Ramaekers et a l , 2002)) to N(7), N(3) and N(l) positions, respectively, in the purine ring. Canonical adenine, the most abundant adenine tautomer, is believed to be the most stable adenine structure in gas phase (Holmen and Broo, 1995; Fonseca Guerra et al, 2006). 3D geometry of a molecule in space primarily determines the shape of the molecule, but does not distinguish the distribution of electrons. It is the electrons which define the molecular properties. Ground electronic states of the adenine tautomers are all in (X^A) states, with closed shells of 35 doubly occupied molecular orbitals (MOs), including 15 outer valence MOs, accordingly. As indicated before (Wang et a l , 2005), adenine and tautomers are slightly non-planar but here for the purpose of simplicity and orbital correlation, the species are treated as planar species with a Cj point group symmetry (Saha et al, 2007a). A Cj point group produces MOs with a' and a" symmetries only, reflecting in-plane a bonding or out of plane (anti-symmetric) % bonding characters. Of the 15 outer valence MOs of the canonical adenine, six MOs possess a " symmetry, whereas nine MOs have an orbital symmetry of a'. The configuration is given by our SAOP/pVQZ model as,

2la'22a '23a 'la "24a '25a '26a D 2a "3a "27 a '4aD28a '5a "29a '6a "(HOMO).

69

16

1412-

o

J

10-

ul

8-

'E>

4-

cu

20-

1

Ade-N9

Ade-N7

Ade-imi1n1n9

Ade-imi1n1n7

Fig. 7 Relative energy of adenine amino N9 and N7 tautomers and adenine imino N1N9 and adenine imino N1N7 tautomers (Saha et al., 2007a)

Here SAOP (Schipper et al, 2000) is one of the recently developed asymptotically correct forms of Vxc in DFT, which is available in the Amsterdam Density Functional (ADF) computational chemistry package (2006). Here the pVQZ basis set is a Slater basis set and has been found to produce good agreement of anisotropic properties to experiment (Chong et al, 2004, Wang et al, 2007a). From screening the symmetry correlated orbital theoretical momentum distributions (TMDs) of the four adenine tautomers in the outer valence space. As observed before (Jones et al, 2006; Fonseca Guerra et al, 2006; Saha et a l , 2007a), not all the in-plane a orbitals exhibit significant changes with respect to the mobile proton positions. The a (i.e., a') orbitals vary more significantly toward the inner valence shell, whereas the n (i.e., a") orbitals (bell shape) remain almost unchanged. Interestingly, the outermost orbitals, i.e., 6a" (HOMO), 29a' (HOMO-1) and 5a" (HOMO-2), do not exhibit significant impact on the proton relocation as they (HOMO and HOMO-2) are dominated by n orbitals. The phenomenon that the frontier orbitals are not always the most active orbitals in reactions has also been observed previously in relation to bio-molecules (Jones et al, 2006; Fonseca Guerra et al, 2006; Saha et a l , 2007a; Wang, Gu and Leszczynski, 2006; da Silva et al, 2006). Figure 8 displays one of the signature orbital TMDs, i.e., orbital 25a' in the outer valence space from our recent SAOP/pVQZ calculations. This orbital differentiates the behavior of the four adenine tautomers caused by a proton transfer, indicating that proton transfer is not a small effect affecting only outermost valence orbitals but may have profound effect on the entire electronic structure of the species.

70

Ade Ade Ade Ade

N7 N9 imi1 N7 imi1 N9

Orbital Momentum (a.u.)

Ade-i9N

Ade-i7N

Fig.8 Orbital MDs in momentum space and corresponding orbital electron charge distributions of the 25a' orbitals of the four adenine tautomers. This orbital (25a') has been identified as one of the important signature orbitals responsible for the tautomerism of adenine.

71

5. Diagnostic of the Most Populated Conformer of Tetrahydrofuran (Sugar) Structural variability and flexibility of bio-molecules such as DNA/RNA are related to their biological functions (Saenger, 1988). The sugar moiety occupies a central position in the structure of DNA/RNA, and is of crucial importance in shaping their structure and dynamics, as evidenced by the striking difference in properties between DNA and RNA which differ only by the chemical nature of sugar. Previous research (Clowney, 1996) indicated that important changes occurring upon the nucleoside conformational transitions are those related to the sugar moiety, whereas the base moiety is relatively rigid structurally (Gelbin, 1996). Tetrahydrofuran (THF) is a prototype of heterocyclic fivemember-ring structures, and an important structural prototype (sugar) of carbohydrates and biological molecules. However, conformations of THF, which are flexible along the pseudo-rotation path as a function of the pseudo-rotation angle cp, have haunted structural chemists for many years due to ambiguous experimental and theoretical results until very recently when Yang et al. (2007) diagnosed the most popular conformation of THF in gas phase, jointly using experimental and theoretical EMS.

Cs conformer of THF

C2 conformer of THF

Fig. 9 Structures of the pair of competitive conformers of Cs and C2 symmetry for tetrahydrofuran (THF) (Yang et al, 2007). It is almost impossible to differentiate the three possible structures of Ci, C2 and Cj for THF without combining experiment with theory. First, their total energy differences were within the error bars of applicable quantum chemistry models; Second, the size of THF is prohibited from higher-level quantum mechanical models such as CCSD(T); Third, most of their properties including dipole moment are close in values among the conformations; and forth, experiments such as microwave and far-infrared spectroscopy and photoelectron spectroscopy (PES) have been unable to identify the most stable structure of THF without contradictions (Rayon and Sordo, 2006). The Cj conformer was theoretically indicated as the most stable conformer of THF using a higher level model of MP2/aug-ccpVTZ (Rayon and Sordo, 2006), without solid experimental evidence. In our recent joint experimental and theoretical EMS study (Yang et al, 2007), the configuration of Ci was found to possess imaginary frequencies so that this conformation was excluded from the candidate conformers. Fortunately, due to

72

the point group symmetries of the C2 and Cs conformers, the highest occupied molecular orbital (HOMO) of the C2 and C^ conformers of THF possess b and a symmetries, respectively, which can be differentiated by EMS using the orbital MDs (Yang et al.2007) shown in Fig. 10.

0.08

^

• Exp

0.06

CO

1

Cs12a'

CD

2

C2 9b

CD >

0.04-^

_C0

^

0.02

0.00 0.0

0.5

1.0

1.5

2.0

2.5

Momentum (a.u.) Fig. 10 Diagnostic of the Cs and C2 conformers of THF based on the symmetries of their HOMOs (Yang et al, 2007).

To resolve the valence space structure of THF, it is critical to further explore the structure and function relationship for this sugar prototype. However, due to experimental difficulties, the outer valence space of the THF conformers has not been fully revealed by EMS measurement at the moment and further experiment with higher impact energies and better resolution is undertaking. From our previous experience in 1,3-butandiene (Saha et al, 2003), it is likely due to thermal motion at the temperature under the experimental conditions (usually room temperature), the pseudo-rotation puckering of the sugar ring could be possible in gas phase. As a result, the Cs and C2 conformers of THF may co-exist in a dynamic balance which can further complicate the experimental signal analysis. We therefore, have taken theoretical examinations on the orbital based behavior in the outer valence space (Duffy et al, 2007) of the C2 and Cs conformers, which hopefully could assist further experimental analysis of the THF conformers in valence space, with insight electronic structural understanding of the conformations of this important bio-molecular fragment.

6. Orbital Signatures of C=C Bond in Sugar Modified Nucleoside Antibiotics (Base+Sugar) Bio-molecules such as nucleosides and analogues are significant in life science. Nucleosides consist of a free base such as cytosine and a furanose type ring (sugar), connecting at the N l position of

73

pyrimidine bases or the N9 position of purine bases by a p-glycosyl bond. Beside the basic nucleosides of adenosine (A), guanosine (G), cytidine (C), thymidine (T) and uridine (U), numerous naturally occurring and chemically synthesized or modified nucleosides—nucleoside analogues exist. As consequences of minor modification in parent nucleosides, the analogues have very similar structural and conformational preferences to their parent nucleosides. Many of them exhibit antibiotic activities and have important medicinal and pharmaceutical applications (Isono, 1991; Matasuda & Sasaki, 2004; Saran, 1998). Nucleoside analogue antibiotics easily get incorporated in growing chains of DNA/RNA by mimicking their parent nucleosides to bring about the inhibition of protein, DNA/RNA syntheses hereby exhibiting a wide variety of antiviral and anti-tumor properties (Saran, 1998). One of the methods in medicinal chemistry over the past several years is to construct "drug-like" small molecules or ligands (Ohlstein, et al, 2000). In a search for novel compounds for genotypespecific effects, a pair of recently synthesized cytidine nucleoside antibiotics, sulfinyl cytidine derivatives (SC-Dl and SC-D2) was reported by Torrance et al (2001). The chemical names of SC-Dl and SC-D2 are given as r,2'-didehydro-3',4'-deoxycytidine (Structure I) and its isomer 3',4'didehydro-2',4'-deoxycytidine (Structure II) in a recent study (Wang, 2007b). Although the drug pair was claimed (Torrance et al, 2001) to meet the standard criteria for drugs established by the National Cancer Institute (NCI, USA, http://wwww.cancer.gov), very little information about the new drugs, such as their chemical names, structures and relative stability, of the pair was known. The isomer pair was originally described by library sources as sulfinyl cytidine (Torrance et al, 2001), but massspectrometric analysis revealed that SC-Dl and SC-D2 represent deoxycytidine analogues containing an unsaturated sugar moiety. At the discovery, it was unable to determine whether the C=C bond resides at either V,T- or 3',4'-positions of the sugar ring, or if a mixture of both isomers was present Torrance et al (2001). As a result, theoretical electron spectroscopy is applied for insight understanding of the structure and functionality of new drugs.

The chemical structures of SC-Dl and SC-D2 differ only by the location of a C=C bond in the sugar ring, as shown in Fig. 11. The C=C double bond makes the sugar ring less flexible for puckering and as a result, both isomers exhibit flat sugar rings. The nucleoside pair possesses unusual sugar structures as shown in the Cambridge Structural Database for nucleosides (Allen, 2002). It was found (Roey et a l , 1993) that such a class of nucleosides with an unsaturated sugar ring often associates with anti-AIDS and anti-cancer drugs. Therefore, insight structural understanding of the drugs is necessary. Fully optimized structures of I and II molecules in 3D space are obtained using B3LYP/6311++G** model. Relocation of the C=C bond, from the CI'=C2' position to the C3'=C4' position in the sugar ring, results in an energy lowering of 5.28 kJ-mol-1, indicating that II is more stable in isolation than its isomer I, from an energy point of view. It is also found (Wang, 2007b) that the positions of the C=C bond do not change the bond lengths noticeably but have significantly changed the shape of the nucleosides in the 3D space. For example, perimeters (Wang et. al, 2005) of the hexagon and pentagon rings, R6 and R5, remain almost unchanged in the isomers. The C=C locations, either C r = C 2 ' or C3'=C4', do not alter the number of C-C and C=C bonds in the respective rings of the isomers. Anisotropic properties such as dipole moments (\i) exhibit a large variation of 1.25 D

74

between the two isomers, from 6.79 D in 1 to 5.54 D in 11, which suggests that the isomer pair maybe able to be characterized by their dipole moment, as Nguyen and Pratt (2006) implemented.

H„H

1',2-D3C

o

.X

O^

«•

J^^. S>-^

OK

5.28 kJ mol 1

3',4'-D3C

Fig. 11 Chemical structures of the SC-Dl (I) and SC-D2 (II) of the drug isomer pair (Wang, 2007a).

Valence ionization spectra of the isomer pair were further investigated from single point calculations using the SAOP/pVQZ model (Schipper et al, 2000; Chong et al, 2004), which shows the approximately satisfactory of the Koopmans' theorem (Gritsenko et al, 2003). The highest occupied molecular orbital (HOMO) and next HOMO contain interesting structural information to differentiate the isomers in their ionization energies. For example, the first ionization energies for 1 and 11 are 9.48 and 10.06 eV, respectively, a difference of 0.58 eV which is within the resolution of a number of experiments such as PES and EMS. Fig. 12 indicates that the orbital electron density contours of 1 and 11 indeed show a very different features in their HOMOs. Further theoretical investigation for their orbital based chemical bonding mechanism is under investigation.

HOMO of Structure I

HOMO of Structure II

Fig 12 Orbital electron density distribution of the HOMOs of Structure I and Structure II. The bonding mechanisms in this orbital is very different: with HOMO of Structure I concentrating on the C=C bond of the sugar moiety whereas with the HOMO of Structure II depositing on the base ring (Wang, 2007a)

75

7. Extension of Atoms-in-Molecules: Fragment in Molecules Progress requires a quantitative understanding of all different fragments, as many biologically relevant molecules have their basic skeleton as an aromatic ring with a short alkyl or alkylamine side chain. In proteins, the smallest amino acid is glycine whereas the smallest and most abundant aromatic residue is L-phenylalanine. Recent data mining experiments have shown that amide-aromatic interactions of phenylalanine are very important in the stabilization of protein residues over large configurational spaces (Duan et al, 2002). L-phenylalanine can be considered as one of the hydrogen atoms of benzene is replaced by L-alanine. The latter (L-alanine) is considered as the product that a hydrogen atom of glycine on the C atom is replaced by a methyl (CH3) group (Falzon et a l , 2006). It is useful if one could determine which orbital or a group of orbitals in both core and valence space approximately belong to which fragment. The knowledge of fragments in bio-molecules will largely enhance rational drug design.

D-H

sia 4QQ-

44a-

CO_H

430-

27H Benzene

alanine

Phenyl

2?QFig 13 Core orbital ionization energy diagrams of benzene, alanine and phenylalanine. The pattern clearly demonstrates an interesting pattern and association of the three species.

76

Ground electronic state configurations of glycine and L-alanine indicate that three more molecular orbitals (MO) are in L-alanine than in glycine: one in the core space and two in the valence space (Falzon et a l , 2006). From our previous work on L-alanine and glycine, we are able to determine which groups of orbitals are responsible for the glycosyl fragment, for the methyl fragment and for the interactions of the two fragments, approximately. Here we extend this method to study the association of canonical L-phenylalanine (Phe-X, ^ A ) , L-alanine and benzene. Figure 13 gives the core orbital energies of the three species generated using the DFT-B3LYP/6-311++G model. It is interesting that the core orbital energy patterns of Phe-X and L-alanine are very much assemble, whereas the core orbitals of benzene are very much "degenerate", which in fact, split into a 1,2,2,1 fold of four lines with better resolution which will be discussed further elsewhere (Wang et al. 2007). From this figure, it is learned (1) the L-alanine "fragmenf contributes to the apparently split into a core orbital energy band of the phenyl fragment of Phe-X, due to the symmetry lowing as a result of the interaction with the alanine fragment; (2) chemical shift in core orbital energies indeed provides some useful information related to the chemical environment of a particular element. In the valence space, similar to L-alanine, glycosyl and methyl (Falzon et al, 2006), the valence orbitals of Phe-X can be divided into alanine related (group I), phenyl related (group II) and mixed (group III) orbitals. Figure 14 (a) gives a representative orbital in the alanine related group I, orbital 22a for alanine and orbital 40a for Phe-X. The orbital TMDs in the same figure indicate that the attachment of the phenyl fragment does not show sufficient impact on this alanine dominant orbital and its 71-like bonding character. Figure 14 (b) shows that a doubly degenerate benzene orbital, 3e2g, splits into two orbitals of 38a and 39a in Phe-X, as a result of the high point group symmetry of benzene (Dgh) reduction (Ci) in Phe-X. The orbital TMDs and electron density distributions of the four related orbitals in this figure, clearly demonstrate the phenyl fragment in L-phenylalanine. Therefore, amino acids are not only important as building blocks of life, but also provide important information for us to understand basic science such as chemical bonding mechanisms.

77

Ala | M 0 22a)

3

4.0x10

Id C

a

n E

2.0x10

3 C

u E a he | M 0 4Da|

Id

o

15 Azimuthal Angle

30 ^f

Fig. 14 (a). Evidences in orbital MDs in momentum space and orbital electron density distributions in position space of the associated orbitals 22« of alanine and 40« of phenylalanine. It has quantitatively demonstrated "fragment in molecule" model.

3 J3

°

2.3x10"'

E • 30

Phe (MO 39a)

Azimuthil Angle ^f

Fig. 14 (b). Orbital MDs in momentum space and orbital electron density distributions in position space of a doubly degenerated orbital 3e2g of benzene, which splits into two orbitals of 38« and 39« in phenylalanine. It has quantitatively demonstrated "fragment in molecule" model.

78

CONCLUSIONS Dual space analysis is a powerful technique associated with electron momentum spectroscopic analysis and interpretation. It consolidates the association between theory and experiment through the predictive power of quantum chemistry and validity power of experiment; connects information in coordinate space and momentum space through a Fourier transform (FT); facilitates interpretation of electronic structure in terms of one-electron concepts through the association of Dyson orbitals to electron binding energies in molecular orbital theory; and achieves quantitative assessment of wave functions (orbitals), which has long been a challenge for quantum chemistry (Eugen Schwarz, 2006). The present review gives a few examples of the applications of DSA to bio-molecules.

ACKNOLEDGEMENT I would like to acknowledge the Vice-Chancellor's Strategic Research Initiative Grant of Swinburne University of Technology (2004-2006), which enabled me to reshape of my research in the past few years. I would like to thank Vice-Chancellor's Research Award in 2006 for the recognition of the work done. Australian Research Council (ARC) is acknowledged for research grants through the Discovery Project and International Linkage Schemes. The Australian Partnership for Advanced Computing (APAC) should be acknowledged for using the state-of-the-art National Supercomputing Facilities. I sincerely wish to thank my advisers and collaborators for their support and contribution to the work in the review. In particular, I wish to thank A/Prof M. J. Brunger for his long term collaboration and constant support in the past decade. The excellent contribution of Dr. M. T. Downton, Dr. C. T. Falzon and Dr. K. Nixon (postdoctoral fellows), Mr. S. Saha and Mr. D. Jones (Ph.D. students) is much appreciated.

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