22

CHAPTER 2

X-RAY CRYSTAL STRUCTURE DETERMINATON

2.1 INTRODUCTION

The X-ray diffraction technique is based on an interference pattern

produced by X-rays passing through a three-dimensional, repeating pattern of

atoms within a crystal. It is the most powerful technique adopted to reveal the

three-dimensional molecular structure, their geometrical description in terms

of bond lengths, bond angles, torsion angles, non-bonded distances,

conformation adopted by the molecule, intra-molecular forces and molecular

packing governed by intermolecular forces (Glusker and Trueblood 2010,

Giacovazzo 2010). As this thesis is concerned with the X-ray crystal structure

determination of biologically important compounds, in this chapter the

methodology and various steps involved in the crystal structure determination,

such as intensity data collection, data reduction, structure solution, refinement

and calculation of geometrical parameters are presented. Conformational

features of the molecules along with intra and intermolecular forces present in

the crystal structure are also discussed.

2.2 PREPARATION AND SELECTION OF SAMPLES

The sample to be used for structure determination must obviously

be a single crystal, in which all the unit cells are identical and should be

aligned in the same orientation, so that they can scatter cooperatively to give a

clear diffraction pattern. Among the various methods of growing single

23

crystals from a saturated solution, the slow evaporation method occupies a

predominant place owing to its versatility and simplicity.

All the samples presented in this thesis were obtained by the slow

evaporation method at room temperature. In this method, the compound

(solute) was dissolved by a suitable solvent or sometimes with mixed

solvents. In almost all cases, the vapour pressure of the solvent above the

solution is higher than the vapour pressure of the solute and therefore, the

solvent evaporates more rapidly and the solution becomes supersaturated

(Zettlemoyer 1976, Buckley 1951, Myerson and Ginde 1993). Therefore the

supersaturated solution is maintained under suitable conditions in such a way

that the rate of evaporation of the solvent is minimized. Best crystals are

usually formed when the solution is free from mechanical vibration and is

allowed to evaporate without disturbance.

The crystals were tested for single crystallinity using a Leica DM

LSP polarizing microscope. These crystals were cut with a sharp scalpel, in

such a way that the size of the crystal should not exceed the diameter of the

X-ray collimator used in the diffractometer. This is to ensure that the sample

has to be completely bathed in X-ray at any orientation. One single crystal

separated from the rest of the sample, is usually glued (with a minimum

quantity of amorphous glue) to a fine glass fibre attached to the goniometer

head. However, samples which are air-sensitive or which degrade by loss of

loosely bound solvent are specially treated by coating them with inert viscous

oil or by sealing them in thin-walled glass capillary tubes.

2.3 INTENSITY DATA COLLECTION AND DATA REDUTION

In general two methods are available for data collection viz.

photographic method and counter method. The collection of crystallographic

diffraction data poses two quite different problems. The first is the

24

determination of the geometry of diffraction for which the size, shape and

symmetry of the reciprocal and direct lattice may be calculated. The second

is the assignment of an observed intensity to every point in the reciprocal

lattice. For routine structural studies the only practical means of collecting a

desired data require that diffraction patterns be obtained from a single crystal

mounted so that the various lattice planes may be brought successively into

reflecting positions. This process must be combined with some means of

recording both the location and intensities of the diffracted X-rays. From

around the1960s, computer-controlled diffractometers became the standard

means of collecting diffraction data, in which a scintillation counter is used as

the detector. These machines are called serial diffractometers. In serial

diffractometers, the detector is positioned to collect the intensity of one

reflection at a time. More recently, X-ray diffractometers equipped with area

detectors, which can simultaneously record all the beams falling in their

detector area in terms of position and intensity. There are various types of

area detectors based on different technologies, each with particular

advantages and disadvantages of size, sensitivity, spatial resolution, speed of

read-out and cost (Stout and Jensen 1989, Clegg 2009).

The intensity data for all the crystals presented in this thesis was

collected by a BRUKER AXS SMART APEX-II diffractometer. The machine

was equipped with graphite monochromated Mo K radiation. The detector is

a SMART APEX-II Charged Coupled Device (CCD) detector. In these

detectors the X-ray energy is first converted to visible light using a

scintillating crystal (phosphor). Visible light from phosphor is taken to the

charge coupled device which converts the light energy into electrical pulse at

each pixel. Normally the transfer of visible photons from phosphor to CCD is

achieved through a fiber optic taper in which a good percentage of energy is

lost.

25

In APEX-II detectors the CCD chip is in close contact with the

phosphor and the energy conversion is almost 1:1. This goniometer in the

SMART APEX-II system has a Eulerian Cradle (three circle geometry). The

crystals were mounted in the goniometer and centered. The crystal to detector

distance was set at 50 mm. Initially a selected number of frames were scanned

and integrated for suitable range of and values. Before collecting the

data, the strategy of the data collection was set from the unit cell parameters

and orientation matrix. The data can be collected by -scan, -scan or both

and -scan methods. In the -scan, is fixed and in the -scan is

fixed, with the range of and angle as 0 to 79º and 0 to 360º, respectively.

The number of frames recorded thus depends on the range of and angles,

and also on the frame width 50. .

During the data collection the crystal is rotated about one axis in

the positive direction and each exposure covers a small angular range of 0.5 ,

with a time span of 10 seconds. Detectors with rapid read-out of the image

can efficiently measure diffraction patterns with relatively narrow angular

slices, but with slower read-out and wide angular frames. In general, the same

reflection may be spread over more than one frame. After the data collection,

the intensity data spread over all frames are integrated. The data were

collected for 100% completeness, with at-least four times redundancy of data

to facilitate a reasonable multi-scan absorption correction. The data collection

typically takes four hours, independent of the size of the structure, however

longer exposure is made for weak scattering samples. Crystal decay was

monitored by repeating thirty initial frames. At the end of the data collection

and analyzing the duplicate reflections, the decay was found to be negligible

for all the crystals studied. The result of the data collection process is a list of

reflections, usually thousands of them, each with lkh indices and a

measured intensity.

26

The extraction of relative structure factor amplitudes from the raw

integrated intensities is the process involved in data reduction. The data

reduction process also includes the merging and averaging of repeated and

symmetry-equivalent measurements in order to produce a unique, corrected

and scaled set of data. The statistical analysis of the complete unique data set

provides an indication of the presence or absence of some symmetry

elements, particularly whether the structure belongs to a centrosymmetric or

non-centrosymmetric system. The Lorentz and polarization corrections are

essential for all the cases, but the absorption correction can be applied

depending on the nature of the compound and the radiation used.

The relationship connecting the observed structure factor and the

raw intensity for each reflection is given by

21

/ LpIkF lkhlkh (2.1)

where k is the scale factor, L is the Lorentz factor 21L sin/ and p is the

polarization factor m22

m2 2122p cos/coscos , since the

beam is partially polarized during monochromatisation. Here m represents

the Bragg angle of a monochromator crystal (6.1 for Mo K ) and

represents the Bragg angle of a reflection. The absorption correction was

carried out by multi-scan procedure using the SADABS (Bruker 2005)

program.

After integration and scaling, the output data (h k l and intensity) is

produced in formats suitable for standard structure analysis packages. Data

collection, cell refinement and data reduction for all the compounds, reported

in the thesis were carried out using APEX2 (Bruker 2005) and SAINT

(Bruker 2005) programs.

27

2.4 STRUCTURE SOLUTION

Having measured and appropriately corrected the diffraction data,

the solution of the structure can be obtained by locating the position of the

atoms. In order to locate the positions of atoms, the electron density has to be

computed at various points. The positions at which the electron density is

maximum, represents the position of an atom. The electron density is the

reverse Fourier transforms of the diffraction pattern. Since the diffraction

pattern of the crystal consists of discrete reflections rather than a diffuse

pattern, the Fourier transform is a summation, and not an integral. The

relation between the electron density and its Fourier transform is given by

h k llkh lzkyhxiFVzyx 2exp1,,, (2.2)

where lkhF is the structure factor, which is the resultant of N waves scattered

by N atoms in the unit cell.

The general expression for the structure factor is

jjj

N

jjlkh lzkyhxifF 2exp

1

(2.3)

where jjj zyx ,, are the fractional co-ordinates of the jthatom, N is the

number of atoms in the unit cell and jf is the atomic scattering factor.

Since lkhF is a complex quantity containing both amplitude and

phase, we can rewrite

lkhlkhlkh iFF exp (2.4)

28

where lkhF is the structure amplitude, and

lkh is the phase of the reflection hkl.

Including the amplitude and phase in zyx ,, , we can write

h k llkhlkh lzkyhxiiFVzyx 2expexp1,, (2.5)

where V is the volume of the unit cell and x, y, z are the fractional coordinates

of any point in the unit cell.

From the above equation, it is clear that the image of the electron

density can be obtained by adding together all the diffracted beams, with their

correct amplitudes and phases; the correct relative phases here include the

intrinsic phases of the waves themselves, relative to the original incident

beam, and an extra phase shift appropriate to each geometrical position in the

image relative to the unit cell origin. Experimentally one can compute the

structure amplitude for each reflection, from the measured intensities. The

relative phases shifts can be calculated as required, but the intrinsic phases

lkh of the different reflections cannot be computed directly from the

experimental data. Thus if one wants to compute electron-density, and to

locate the position of atoms the phase lkh is necessary. This is called

‘PHASE PROBLEM’ in crystallography.

Depending upon the number and nature of atoms present in the unit

cell, different methods have been used to tackle the phase problem (Stout and

Jenson 1989, Clegg 2009, Shmueli 2007) viz., direct methods, heavy atom

method, isomorphous replacement method and the anomalous dispersion

method. Since the compounds of our interest contain only light atoms, direct

methods were employed for solving the structure using SHELXS97

29

(Sheldrick 1997) program. This program is a general one and is efficient for

all space groups in all settings, and there are effectively no limits on the

number of reflection data, atoms, phases refined in direct methods or

scattering factor types. The program is more accurately described as a

multiple-permutation single-solution procedure.

2.4.1 Direct Methods

Direct methods relates the intensities and phases by mathematical

means (Giacovazzo 2010, Ladd and Palmer 1977, 1980, Woolfson 1997).

Although these methods have some limitations in their applications when the

number of non-hydrogen atoms in a molecule is greater than 50, for smaller

structures the success rate of these methods is close to 100%. The direct

methods routine is based on the random start multi-solution technique.

In direct methods there are two imposed conditions that restrict the

relative phase angles viz. the electron density is always positive and the atoms

are spherically symmetric. Possible phase angles are constrained by these two

conditions so that relative phase angles mainly depend on mathematical

expressions for the Fourier series. In the initial stage, atoms are assumed to be

of point atom type. The fall-off of intensity at high scattering angles is due to

atomic size and atomic vibrations lkhF is related to lkhE , which do not vary

with sin .

2.4.1.1 Direct methods procedures

The following procedures are adopted in solving the structure using

direct methods.

30

1. Conversion of observed structure factors lkhF to

normalized structure factors: The conversion of observed

structure factors lkhF to normalized structure factors lkhE ,

using the following relation (Ladd and Palmer 1980)

222/ jlkhlkh fFE (2.6)

where is an integer which is generally one, but may assume

other values for special sets of reflections in certain space

groups. Also, only high lkhE values (greater than 1.5) signify

greater validity of the probabilistic estimate.

2. Setting up of the phase relations: The magnitudes lkhE of

the normalized structure factor are uniquely determined by

crystal structure and are independent of the choice of origin,

however values of the phases lkh depend on choice of the

origin. There exists certain linear combination of phases,

which are called structure invariants (International Tables for

Crystallography 2006), whose values are determined by the

structure alone and are independent of the choice of origin. In

shifting the origin by a vector, the phases turn out to be origin

dependent while amplitudes are not. But there are certain

specific phase relations viz, triplet (three phase structure

invariant) relation, given by LKH such that H+K+L=0

and quartet (four phase structure invariant) relation, given by

PNML such that L+M+N+P=0, that do not change

with shift in origin.

31

3. Choosing a starting reflection: A convergence procedure is

used to determine the starting set for the phase relations. Only

strong lkhE values are chosen in the generation of invariants

so that the reliability of the probabilistic estimates has a direct

relation to the normalized structure factor magnitudes entering

in the triplets or quartets. Sets of three Bragg reflections are

selected with indices that satisfy the triple-product sign

relationship 2 formula.

KKHKH (2.7)

where H is the relative phase angle of the Bragg reflection

hkl.

4. Phase propagation or phase extension: The phases of the

above small set of reflections are now assumed to be known

and knowing the values of the two phases and sum of the three

phases, the value of the unknown phase can be determined.

This procedure is called the phase propagation or phase

extension. This propagation and phase refinement are carried

out using tangent formula of Karle and Hauptman (Schenk

et al 1987).

sintan

cos

j j j jj

j j j jj

k h k k h kk

h

k h k k h kk

E E

E E (2.8)

5. Calculation of best set of phases: Depending on the choices

of the phase values for the reflections chosen for the origin

and enantiomorph, the direct methods procedures become

multi-solution in nature from which the correct solution can be

32

picked up. Before computing an E-map, the set with the

lowest value for the combined figure of merit is selected as the

correct one. The combined figure of merit is given by

CFOM = ]0[ nWNQUALorR , (2.9)

whichever is larger

with 22 / estest WWR (2.10)

and NQUAL = 54321

54321

EEEEE

EEEEE

****

**** (2.11)

where the weight w is 51 est/ , is the reliability

coefficient and wn is a structure dependent constant. The best

10% of the subset phase permutation as judged by R is then

refined using the full set of reflections. For a correct solution

NQUAL will approach -1.

6. Computation of E-maps: After the determination of phases

H and confirming them by CFOM, an E-map can now be

computed using the HE values for the best phase set. The

heights of the peaks in the E-map will be in proportionate to

the atomic number of the atoms in the unit cell.

By this method almost the entire structure can be revealed. Thus the

structure solution will reveal the positions of all the non-hydrogen atoms.

However in case of any incompleteness, the existing model has to be refined

for few cycles (i.e. isotropic refinement) and a difference Fourier map will

reveal the rest of the atoms. For an initial correct solution the R-values ranges

from 20-30%.

33

2.5 STRUCTURE REFINEMENT

The data obtained from an X-ray diffractometer experiment

produce a set of structure factor magnitudes oF and with the proposed model

the structure factor magnitudes cF can be calculated. The combination is

used to get the best possible fit between the observed and calculated structure

factors. Specially, it is necessary to find the atomic coordinates (xj,yj,zj) and

functions that give maximum agreement with the observed structure factor.

The ultimate purpose is therefore to refine three positional parameters and up

to six thermal parameters for each atom to give the better fit with the

experimental data. The refinement stage of a structure analysis begins with a

complete trial structure containing all the atoms.

If the atoms of the structure are approximately in the right

positions, then there will be at least some degree of resemblance between the

calculated diffraction pattern and the observed one. This approximation can

be achieved by several structure refinement processes viz. full-matrix

least-squares method, block diagonal least-squares method, rigid body

refinement, energy minimization technique, simulated annealing technique,

maximum entropy method or the maximum likelihood method. Among them,

the full-matrix least-squares refinement techniques is the conventional one

and widely used in small molecular structure refinement using the program

SHELXL97 (Sheldrick 1997a). The least-squares refinement uses the square

of the difference between the observed and calculated structure factor

amplitudes as a measure of their disagreement and adjust the parameters so

that the total disagreement is a minimum. The refinement based on 20F using

all data provides a good result for weakly diffracting crystals and in particular

for pseudo-symmetry problems.

34

The residual factor or reliability index defining the correctness of

the model is given by

hkl0

hklC0

F

FF1R (2.12)

where 0F is the observed structure factor amplitude and CF is the

calculated structure factor amplitude. The summation is made over all the

observed reflections 00 F4F . The lower the R value, the greater is the

accuracy of the molecular model. A suitable weighting scheme is applied at

the end of refinement procedure and the weighted R-factor is given by

21

220

22202

Fw

FFwRw

i

Ci (2.13)

The goodness of the fit (S) is given by

21222

0 / pnFFwS c (2.14)

with bPPaFw 220

2/1 (2.15)

where P = [2Fc2+Max(Fo

2, 0)]/3, n is the number of reflections, p is the total

number of parameters refined, a and b are constants.

2.6 CALCULATION OF GEOMETRICAL PARAMETERS

The determination of molecular geometry is of vital importance to

our understanding of chemical structure and bonding. The crystal structure

determination provide us the unit cell geometry, symmetry (space group) and

35

the positions of all the atoms in the unit cell (three coordinates each), together

with their isotropic (one) and anisotropic (six) displacement parameters. From

the atomic coordinates, unit cell geometry and symmetry, many geometrical

parameters such as bond lengths, bond angles and torsion angles, etc. can be

calculated.

Bond Length: For the triclinic system, the distance between two atoms

considered to be bonded together, with fractional atomic coordinates

111 ,, zyx and 222 ,, zyx , is given by the law of cosines in three dimensions

as

yxbazcybxaL cos2222

21

cos2cos2 zybczxca (2.16)

where ,,,, cba and are the unit cell parameters; 2121 , yyyxxx

21 zzz .

The above equation can be applied for any crystal system to

calculate the bond lengths. These parameters help us to identify the nature of

chemical bonds (triple, double, partially double or single bond) present in the

molecule.

Bond angle: The angle between the bonds A B and B C formed by three

atoms A B C, as shown in Figure 2.1 is calculated by using the formula

BCBA

ACBCBA

rrrrrcos

2

2221 (2.17)

36

Figure 2.1 Bond angles

Bond angles are useful to find the type of hybridization of a

particular atom.

Torsion angle: The torsion angle is the angle of inclination between the two

planes defined as ABC and BCD of the four atoms A, B, C and D. The

apparent angle between two bonds A B and C D when viewed along the

B-C bond for a connected sequence of atoms A B C D, referred as

torsion angle, is given by

21

21

NNNN (2.18)

where N1 and N2 are normal to the ABC and BCD planes, respectively.

PARST (Nardelli 1995) and PLATON (Spek 2003,2009) programs were used

for the calculation of geometrical parameters in all the structures studied.

2.7 RING CONFORMATIONS

Ring conformations can be described by torsion angles, atomic

deviation from least-squares planes or angles between least-squares planes.

They can also be analysed in terms of asymmetry parameters and puckering

parameters.

rBA

rBC

rAC

37

The presence of a mirror plane lying perpendicular to the plane of

the ring and a two-fold symmetry lying in the plane of the ring predicts the

type of conformation of the ring. The possible conformations of the five- and

six-membered rings are shown in Figures 2.2 and 2.3, respectively. The

mirror and the two-fold symmetry are governed by symmetry equations,

21

m

1i

2ii

S mC

'

(for mirror asymmetry) (2.19)

and

21

m

1i

2'ii

2 mC (for two-fold asymmetry) (2.20)

where ', are symmetry related torsion angles and m is the number of

individual comparisons.

The five-membered ring can adopt three types of conformations viz.

planar with five two-fold and five mirror symmetries, envelope with a mirror

symmetry and half-chair with a two-fold symmetry.

The six-membered ring can adopt six types of conformations viz.

planar having six two-fold and six mirror symmetries, chair having three

mirrors and three two-fold symmetries, boat having two mirror symmetries,

twist boat having two two-fold symmetries, sofa having one mirror symmetry

and half-chair having one two-fold symmetry. In practice, conformations are

described from the asymmetry parameters (Nardelli 1983) and puckering

parameters (Cremer and Pople 1975), which give the extent of deviation of

38

the ring from ideal conformations. Calculation of these parameters, are

carried out using the program PLATON (Spek 2009).

Figure 2.2 The three most symmetric conformations observed in the five-membered rings (Duax et al 1976). Symmetries are indicated on the right

39

Figure 2.3 The most commonly observed conformations of six-membered rings (Duax et al 1976). The symmetries are indicated on the right

40

Any deviation from the ideal ring conformations is described by

puckering parameters suggested by Cremer and Pople (1975). The

conformation of the n-membered ring is uniquely defined by its n-3 puckering

parameters. For a six membered ring there are three puckering degrees of

freedom. These are described by the single amplitude phase pair (q2 and 2)

and a single puckering coordinate q3. These polar coordinates described by

the ‘spherical polar set’ (Q, , ), where Q is the total puckering amplitude and

is the angle (0 ) such that

q2 = Q sin (2.21)

q3 = Q cos (2.22)

This coordinate system permits the mapping of all types of

puckering. The polar coordinate values for the special conformation of the

six-membered rings are given below:

Chair = 0.0

Half-chair = 50.8 = k 60 + 30

Envelope = 54.7 = k 60

Boat = 90.0 = k 60

Twist-boat = 90.0 = k 60 + 30

where k = 0, 1, 2, 3, 4, 5.

2.8 INTER AND INTRAMOLECULAR INTERACTIONS

Different types of inter- and intramolecular interactions such as

hydrogen bonding (Desiraju 2000, 2002, Hunter et al 2001, Row 1999,

Aakeroy 1997, Koch and Popelier 1995), C H… interactions

41

(Takahashi et al 2000, Prasanna and Row 2000, Nishio et al 1995, Umezawa

et al 1999), stacking interactions (Sharma et al 1993, Hunter and

Sanders 1990, Desiraju and Gavezzotti 1989) short contacts between the

atoms and van der Waals interactions stabilize the molecules in the crystalline

state. The existence of C H…O type hydrogen bonds in crystals is evident

from the study of Steiner (2002), Desiraju and Steiner (1999), Desiraju

(1991), Jeffery and Saenger (1991), Berkovitch-Yellin and Leiserowitz

(1984).

Hydrogen bonding is formed between two electronegative atoms

(donor and acceptor), where the hydrogen atom is bonded to one of them. The

usual convention for the representation of the hydrogen bond is D H…A

where D is the donor and A is the acceptor. The hydrogen bonds are highly

directional and the D H…A angle should be 180º for an ideal one. The most

important geometrical characteristics of hydrogen bonds are that the distance

between the hydrogen and acceptor atom is shorter than sum of their van der

Waals radii (Taylor and Kennard 1982).

The criteria, which is generally used to identify the hydrogen bond

(Desiraju and Steiner 1999) are Å50.0.... ARDRADd ,

Å12.0.... ARHRAHd and 100...AHD ,where D is the donor, A

is the acceptor, DR is the van der Waals radius of donor atom, AR is the

van der Waals radius of acceptor atom, HR is the van der Waals radius of

the hydrogen atom, ADd ..... is the distance between the donor and acceptor

atom and AHd ..... is the distance between the hydrogen and acceptor atom.

Some of the properties of strong and weak hydrogen bonds are detailed in

Table 2.1.

42

Table 2.1 Some properties of strong and weak hydrogen bonds (Desiraju and Steiner 1999)

Properties Strong Weak Non-bond

Bond energy (-Kcal / mol) 15-40 4-15 <4

Examples POOHP

NHN

FHF

.........

......

POHOCOHNCOHO

.........

OHOHO

OHC

...

...

...

Bond Lengths HDAH HDAH ... HDAH ...

Lengthening of ÅHD 0.05 – 0.2 0.01 – 0.05 010.

Å)rangeADd (... 2.2 – 3.0 3.0 – 3.5 3.6 – 4.0

AHd ... range (Å) 1.2 – 2.5 1.5 – 2.5 2.6 – 3.0

AHD ... range (°) 175 – 180 130 – 180 90 – 180

Effect on crystal packing strong Weak Non-bond

van der Waals interactions are formed due to the weak attractive

forces between uncharged atoms or molecules. The van der Waals forces are

short-range forces i.e., they are significant only when the molecules are very

close to one another. The van der Waals forces are used for non-specific

attractions between two atoms that are close to each other. These interactions

depend on the distance between the respective atoms (or atom groups or

molecules). At too close distance, repulsive forces are dominating

(overlapping of electron shells). vander Waals attractions are additive and

have thus a much greater impact on macromolecules than on small molecules

(Steiner and Saenger 1993).

The crystal structures presented in this thesis are found to have

O H…O hydrogen bonds, and weak C H…O and C H…N intermolecular

interactions. The van der Waals radii used for C=1.70, Cl=1.75, Br=1.85,

N=1.55, O=1.52, F=1.47 and S=1.80 Å. For hydrogen bonds, the H…A

43

distances are less than 2.6 Å and the range of D…A distances is 2.2-3.0 Å. If

H…A distances are less than 2.6 Å and D…A distances lie in the range 3.0-

3.5 Å then the interactions are considered as weak intermolecular interactions.

2.9 GRAPH SET – DEFINITIONS

Etter (1991) formulated a useful method for describing hydrogen-

bond patterns in crystal structures based on graph set notation. Graph sets tell

how many donors and acceptors are used in a hydrogen-bonded pattern and

what the nature of the pattern is. The most remarkable feature of the graph set

approach to analyse hydrogen bond patterns is that even complicated

networks can be reduced to combinations of four simple patterns, viz.,

(i) chain (C)

(ii) rings (R)

(iii) intramolecular hydrogen patterns (S) and

(iv) finite patterns (D)

Specification of a pattern is augmented by a subscript ‘d’

designating the number of hydrogen-bond donors and a superscript ‘a’ giving

the number of hydrogen-bond acceptor. The graph set descriptor is then

given as Gda (n), where G represents one of the four possible designators and

‘n’ representing the total number of atoms involved in the motif is called the

degree of the pattern and is specified in parenthesis (Bernstein et al 1995).

The analysis of hydrogen-bonding patterns into these four simple categories

can lead to important insights regarding the patterns of recognition between

both like and unlike molecules.

44

2.10 SOFTWARES USED FOR CRYSTAL STRUCTURE

DETERMINATION

The intensity data for all the crystals presented in the thesis were

collected by a Bruker AXS SMART APEX-II diffractometer equipped with

graphite monochromated Mo K radiation ( = 0.71073Å) using the scans

mode. Intensities were corrected for Lorentz and polarization effects and

absorption effects by using the SADABS (Bruker 2005) program. The

structures were solved by direct methods using the SHELXS97 (Sheldrick

1997) program. The structures were refined by the full-matrix least-squares

technique using the SHELXL97 (Sheldrick 1997a) program. The geometrical

parameters were calculated using PLATON (Spek 2009) and PARST

(Nardelli 1995), and the molecular and packing diagrams were drawn using

the program SHELXTL (Sheldrick 1998) and PLATON (Spek 2009).