i

AB INITIO STUDIES OF A PENTACYCLO-

UNDECANE CAGE LACTAM

by

Thishana Singh

Submitted in partial fulfillment of the requirements for the degree of

Master of Technology

in the Department of Chemistry,

Faculty of Engineering, Science and the Built Environment,

Durban Institute of Technology, Durban, May 2003.

ii

DECLARATION

I, Thishana Singh, declare that unless indicated, this dissertation is my own work and it

has not been submitted for a degree at another Technikon or University.

________________________

T. Singh

_____day of______________2003

APPROVED FOR FINAL SUBMISSION

________________________ ________________________

Supervisor: Dr. K. Bisetty (Ph.D.) Co-supervisor: Dr. H.G. Kruger (Ph.D.)

________________________

Date

iii

ACKNOWLEDGEMENTS

I would like to thank my supervisors Dr. K. Bisetty and Dr. H.G. Kruger for their

assistance, guidance, patience and much appreciated words of encouragement

throughout the duration of this research project.

My sincere gratitude also goes to:

(i) My friends and colleagues at the Durban Institute of Technology,

Department of Chemistry, for their support, encouragement and

assistance.

(ii) The National Research Foundation (NRF), M L Sultan Technikon

Research Center for financial assistance.

(iii) De Beers Educational Trust Fund for the purchase of a desk top

computer.

(iv) The University of Natal, Durban for the generous use of computer time

on the DEC Alpha computer workstation.

A special thanks to my parents for their continuous support and encouragement

throughout the duration of my studies.

"Jai Shree Krishna"

iv

ABSTRACT

The purpose of this study is to utilize computational techniques in the determination of

the mechanistic pathways for the one-pot conversion of a pentacyclo-undecane (PCU)

dione 1.1 to a pentacyclo-undecane cage lactam 1.2.

OO

NaCN

H2O

OH

C O

NHHO

1.1 1.2

In pursuance of this objective, the ab initio quantum mechanical level of theory was

employed. The primary goal of this study was to compute the relative difference in

energies for the reactants, products and transition-states of the proposed mechanistic

pathways. The energy values obtained were used to predict the thermodynamic and

kinetic pathways of the mechanism. All calculations were performed using the

GAUSSIAN 98 series of programs, and GAUSSVIEW was used to visualize the

transition-state structures.

Full geometry optimizations were performed at the Hartree-Fock (HF) level of theory

using the 3-21+G* basis set. In addition, the transition-states were established using a

SCAN technique to obtain a starting structure. Transitions states were verified by using

second-derivative analytical vibrational frequency calculations and the visual inspection

of the movement of atoms associated with the transition.

Hess's Law was applied to compute the heats of formation. It was found that two

transition structures in the gas phase had abnormally high energies. However, these

energies were found to be considerably lower in the presence of a solvent molecule.

Furthermore, it was observed that the one-step conversion of the dione 1.1 to the lactam

1.2 proceeded via a single transition-state.

Previous experimental work found that the reaction proceeds through a cyanohydrin

intermediate which in all likelihood represents the rate determining step. Sound

v

arguments exist to demonstrate that the computationally determined rate-determining

step agrees with the experimentally observed rate-determining step.

vi

TABLE OF CONTENTS

Declaration ...................................................................................................................... ii

Acknowledgements ........................................................................................................ iii

Abstract .......................................................................................................................... iv

Table of contents ............................................................................................................ vi

List of figures ............................................................................................................... viii

List of tables ................................................................................................................. viii

List of Abbreviations ..................................................................................................... ix

Chapter 1 ......................................................................................................................... 1

1. INTRODUCTION ................................................................................................ 1

1.1 Computational Chemistry and Molecular Modeling ....................................... 1

1.2 Pentacyclo-undecane (PCU) Cage Compounds............................................... 2

1.3 Lactam formation ............................................................................................. 4

Chapter 2 ......................................................................................................................... 9

2. THEORETICAL TOOLS FOR MOLECULAR ORBITAL

CALCULATIONS ............................................................................................... 9

2.1 Molecular Orbital Theory ................................................................................ 9

2.2 Molecular Mechanics ....................................................................................... 9

2.3 Electronic Structure Methods ........................................................................ 10

2.3.1 The Ab Initio Method .............................................................................. 11

2.3.2 Semi-Empirical ........................................................................................ 12

2.3.3 Density Functional Theory (DFT) Methods ............................................ 12

2.3.4 Basis Sets ................................................................................................. 13

2.3.4.1 Minimal Basis Sets ............................................................................... 14

2.3.4.2 Split Valence Basis Sets ....................................................................... 14

2.3.4.3 Polarised Basis Sets .............................................................................. 15

2.3.4.4 Basis Sets Incorporating Diffuse Functions ......................................... 16

2.3.5 Hartree-Fock Theory ............................................................................... 16

vii

Chapter 3 ....................................................................................................................... 19

3. TRANSITION STRUCTURE MODELING .................................................. 19

3.1 Transition-state modeling with empirical force-fields ................................... 20

3.2 Locating minima on the seams of intersecting semi-empirical PES .............. 22

3.3 Transition-structure modeling of a PCU Cage Lactam using ab initio methods

........................................................................................................................ 23

Chapter 4 ....................................................................................................................... 26

4. COMPUTATIONAL DETAILS EMPLOYED ............................................... 26

4.1 The GAUSSIAN 98 Program ........................................................................ 26

4.2 The GaussView Program ............................................................................... 27

4.3 The SCAN Calculation .................................................................................. 27

4.3.1 Commands used during a SCAN or a TS Search .................................... 28

4.4 Calculation Details ......................................................................................... 29

5. RESULTS AND DISCUSSION ......................................................................... 30

5.1 Introduction .................................................................................................... 30

5.2 Local minima on the energy profile ............................................................... 33

5.3 The Transition Structures (TS) ...................................................................... 34

5.3.1 Transition Structure 5.3.1 ........................................................................ 36

5.3.2 Transition Structure 5.5 ........................................................................... 39

5.3.3 Transition Structure 5.7.1 ........................................................................ 41

5.3.4 Transition Structure 5.10 ......................................................................... 47

5.3.5 Transition Structure 5.12 and 5.13 .......................................................... 49

5.4 Transition structure modeling with solvent molecules .................................. 56

5.5 Calculation of Heats of Formation ................................................................. 61

Chapter 6 ....................................................................................................................... 62

6. CONCLUSION ................................................................................................... 62

APPENDIX 1................................................................................................................. 63

Scheme of reaction ...................................................................................................... 64

References ...................................................................................................................... 67

SUPPLEMENTARY MATERIAL: A CD accompanying this thesis includes the following:

Text containing Chapters 1-6 (including References).

Cartesian coordinates of all the 3-D structures from Chapter 5.

Frequency calculations of the TS's.

viii

LIST OF FIGURES

Figure 3.1 Points on a simple reaction coordinate ....................................................... 19

Figure 5. 1 Modified mechanism for the conversion of the dione 5.1 to the lactam 5.2

.................................................................................................................... 31

Figure 5. 2 Calculated reaction profile for the proposed mechanism. .......................... 32

Figure 5.3 Graphical representation of Energy vs Reaction Coordinate for structure

5.3.1 ............................................................................................................ 37

Figure 5.4 Graphical representation of Energy vs Reaction Coordinate for structure 5.5

.................................................................................................................... 40

Figure 5.5 Graphical representation of Energy vs Reaction Coordinate for structure

5.7.1 ............................................................................................................ 42

Figure 5.6 Graphical representation of Energy vs Reaction Coordinate of the zoomed

in (2.03 Å to 1.78 Å) relaxed scan for structure 5.7.1 ................................ 44

Figure 5.7 Graphical representation of Energy vs Reaction Coordinate of the zoomed

in (1.83 Å to 1.35 Å) relaxed scan for structure 5.7.1 ................................ 45

Figure 5.8 Graphical representation of Energy vs Reaction Coordinate for structure

5.10 ............................................................................................................. 47

Figure 5.9 Graphical representation of Energy vs Reaction Coordinate for structure

5.12 ............................................................................................................. 50

Figure 5.10 Graphical representation of Energy vs Reaction Coordinate for structures

5.12 and 5.13. ............................................................................................. 52

Figure 5.11 Graphical representation of Energy vs Reaction Coordinate for structure

5.13 ............................................................................................................. 53

Figure 5.12 Graphical representation of Energy vs Reaction Coordinate for structure

5.12 ............................................................................................................. 55

Figure 5.13 Calculated reaction profile for the proposed mechanism. ........................... 60

LIST OF TABLES

Table 5.1 Calculated energies of the local minima. ....................................................... 33

Table 5.2 Calculated energies of the transition structures. ............................................ 35

Table 1.1 Summary of Energies ..................................................................................... 63

Table 2.1 Heats of Formation ........................................................................................ 66

ix

LIST OF ABBREVIATIONS

CPU Central Processing Unit

DEC Digital Equipment Corporation

DFT Density Functional Theory

G98W Gaussian 98 Windows

GTOs Gaussian-Type Orbitals

GUI Gaussian User Interface

HF Hartree Fock

IR Infra Red

LCAO Linear Combination Atomic Orbitals

MM Molecular Mechanics

NMR Nuclear Magnetic Resonance

PCU Pentacyclo-Undecane

PES Potential Energy Surface

RFO Rational Functional Optimization

RHF Restricted Hartree Fock

SCF Self Consistent Field

SE Semi-Empirical

SP Single Point

STOs Slater-Type Orbitals

STQN Synchronous Transit-Guided Quasi Newton

TS Transition-State/Structure

UV Ultra Violet

x

1

CHAPTER 1

1. INTRODUCTION

1.1 Computational Chemistry and Molecular Modeling

The terms “theoretical chemistry”, “computational chemistry” and “molecular

modeling” are used interchangeably and indeed most molecular modelers use all three

concepts to describe various aspects of their research.

“Theoretical chemistry” is often considered synonymous with quantum mechanics,

whereas computational chemistry encompasses not only quantum mechanics but also

molecular mechanics, minimizations, simulations, conformational analysis and other

computer-based methods for the understanding and the prediction of the behaviour of

molecular systems. However theoretical chemistry is a subfield of chemistry where

mathematical methods are used in combination with the fundamental laws of physics to

study chemical processes.1 In particular, this involves the breaking of new ground that

ultimately leads to the writing of new mathematical codes or software that can model

certain aspects of a chemical structure.

Computational chemistry has therefore become one of the mainstays of modern

industrial and academic chemistry that makes use of the established codes or software to

study chemical systems. The ever-increasing power of modern computers coupled with

the development of new theoretical approaches can be used for accurate and precise

prediction of molecular properties.2 It is interesting to note that computational

chemistry accounts for roughly a third of the super computer usage worldwide.

Computer methods are used extensively to solve chemical problems that would be

intractable or even impossible experimentally.3

Computer-aided molecular design became a subject worthy of discussion in the media

around 1981, with the advancement of sophisticated computer graphics hardware.3 The

general aims of computational chemistry is the characterization and the prediction of

chemical structures and their stability; the prediction of NMR, IR and UV spectra, the

prediction of thermodynamic data, and the simulation and modulation of reaction

2

courses.4 To achieve this computational chemists are using advanced computer

software that enables them to gain insight into chemical processes and to avoid time-

consuming and expensive experiments.3 This approach does not replace the traditional

wet chemistry experiments but it is a powerful aid in the understanding of experimental

observations and the prediction of new reaction pathways. Some methods can be used

to model not only stable molecules, but also short-lived, unstable intermediates and

even transition-states which are required for kinetic information. In this way, they can

provide information about molecules and reactions that may be impossible to obtain

experimentally. Computational chemistry is therefore both an independent research

area and a vital adjunct to experimental studies.

1.2 Pentacyclo-undecane (PCU) Cage Compounds

During the past half-century,5,6,7,8

many research groups focused on the synthesis and

chemistry of novel polycyclic cage molecules. Davis and co-workers9 were responsible

for discovering that 1-amino-adamantane 1.3, commonly known as amantadine, exhibits

antiviral activity thus realizing that polycyclic cage molecules also have the potential as

biologically active agents.

An unexpected observation10

of the biological activity profile of amantadine revealed

that it could be beneficial to patients with Parkinson‟s disease. The hydrocarbon cage

of amantadine has the ability to cross the blood-brain barrier and to enter the central

nervous system10

due to the hydrophobicity of the "cage" despite the fact that the amino

group is protonated at physiological pH. Drugs containing hydrocarbon cage moieties

promote their transport across cell membranes and increase their affinity for lipophilic

regions in receptor molecules.11

While the hydrophobicity of the cage facilitates transport of the drug across membranes,

the size and stability of the cage inculcate the drug with a structural property which

3

results in controlled release of the active ingredients of the drug, namely, stability

towards degradation. In practice this translates into slow metabolism of the drug. The

important implications of this is that the intervals between drug administration is

increased.12

Another factor that was found to influence the rate of release of the active

ingredient and the potency of the drug was the presence of the amantadine substituent in

the drug. It has been shown that the inclusion of amantadine has given rise to longer

time over which the drug is effective, greater potency of the drug and faster drug action.

Furthermore the nature of the substituent influences the specificity of the drug to

antibacterial13

, anabolic14

and analgesic action.15

A number of cases16,17,18

have recently demonstrated the potential therapeutic value of

novel pentacyclic cage compounds. These compounds have promising potential as an

important new class of medicinal and pharmaceutical agents and might extend the

existing range19,20,21

of bio-active pentacyclo-undecane compounds. Further

investigation is required into the influence of the unique steric distribution of important

functional groups around a rigid cage structure on the pharmacological activity.

The Diels-Alder 1.6 adduct of cyclopentadiene 1.4 and p-benzoquinone 1.5 produces

the PCU dione 1.1. The reaction in which the dione 1.1 is synthesized is carried out by

intramolecular photocyclisation.22

h

OO

OO

+

O

O

1.4 1.5 1.6 1.1

Treatment of the dione 1.1 with Strecker reagents (HCN, NH4OH) unexpectedly

produced23

the -lactam compounds 1.2a-1.2c. Strecker reactions normally produce

cyanohydrins or amino nitriles.24

4

O

O

C

NH

OH

O

R

C

N

OH

OH

R

Lactam Lactim1.1 1.2 a, R=OH1.2 b, R=CN

1.2 c, R=NH2

811811

The mechanism of this unique one pot conversion23,25,26,27

is not well understood. The

mechanism proposed by the authors23,25,26

was based on basic chemical principles and

is discussed below.

1.3 Lactam formation

In a previous study28

it was shown that the dione 1.1 is easily hydrated to form the

hydrates 1.7 and 1.8 in a 4:1 ratio. Thus it can be expected that this phenomenon should

also play a significant role in the nucleophilic addition reactions on the carbonyl groups

of the dione 1.1 in aqueous media.

It can subsequently be assumed that both 1.1 and 1.9 (in Scheme I shown below) can

participate in the formation of the dihydroxylactam 1.2. Nucleophilic attack is expected

to take place on the exo face of the carbonyl groups27

in the dione 1.1 or the hydrate 1.9

as a result of the proximity of the groups and could lead to the formation of 1.11.

Transannular cyclisation of 1.11 is expected to form the cyclic ether 1.12. Scheme I

shown below was one of the two proposed mechanistic pathways, based on basic

chemical principles and intuition.23,25,26,27

5

-

1.121.11

1.10

1.9

H2O

H2ONaCN

H2O

H2ONaCN

1.1

OHOH

O

CN

OH

O

CN

OH

OHOH

CN

OH

O

H2O

Scheme I: Conversion of the dione to the cyclic ether

It was assumed that the cyclic ether 1.12 plays an intermediate role in the conversion of

the dione 1.1 to the dihydroxylactam27

1.2, since the “inversion” of a nitrile group can

be explained as in Scheme II shown below.27

The authors later showed27

that the

cyanohydrin 1.11 and 1.12 can be converted to the corresponding hydroxyl lactam 1.17

upon treatment with aqueous NaOH, providing experimental proof for their assumption

above.

The explanation27

for the conversion of 1.12 to 1.2 is discussed in Scheme II below.

Under basic reaction conditions, ring cleavage of the cyclic ether 1.12 forms the

intermediate 1.13 which is converted to intermediate 1.14. The electron deficient nitrile

carbon atom of the endo-orientated cyano group in 1.13 is in an extremely favourable

position to suffer attack from the nearby negatively charged oxygen atom. Intermediate

1.14 rearranges to form intermediate 1.15. Cyclisation of the intermediate 1.15 results

in the formation of lactim 1.16 and by implication the lactam 1.2.27

6

H2O

1.151.161.2

C

OH

OH

ON

1.14

C

O

OH

O

N

H

OH

C

OO

N

H

1.13

OH

C

NH

OH

OH

O

1.12

C

N

OH

OH

OH

CN

OH

O

H2O

--

-

-

Scheme II: Conversion of the cyclic ether

The above explanation does not account for the formation of a compound such as the

cyano hydroxylactam 1.2b (Scheme III).23,26

The nucleophilic attack of the hydroxide

on the cyclic cyanohydrin 1.12 is shown is Scheme III. This is necessary to “invert” the

cyanide group and is expected to be combined with the loss of the hydroxide group in

the cyclic cyanohydrin 1.12, whereby the cyanohydrin 1.19 should be formed. The

endo cyano group in 1.20 has an electron deficient carbon atom which is in an

extremely favourable position to suffer attack from the nearby negatively charged

oxygen atom thus producing the intermediate 1.21 and subsequently 1.22. The

rearrangement of 1.22 to the -cyano cation 1.23 is a postulated rearrangement and is

not a controversial one. This is so since -cyano cations of the general formula shown

in 1.24 are significantly stabilized by charge delocalisation through resonance structures

such as 1.25, even though this requires a portion of the charge to reside on a divalent

nitrogen.29,30

When attached to very unstable cations30

then only is the -donor effect

of cyano substituents manifested. The rearrangement proposed in Scheme III is

promoted since the negative charge on the nitrogen atom of 1.23 is sufficiently

stabilized by the adjacent carbonyl group to facilitate the rearrangement.

7

+

+

+

-

--

-OH

CN

-

HOC O

CN

N

OOHNC

O

HOCN

HOC

O

NH C

N

CNC O

HO

HN

CNC O

HO

N

C C N

R

R

C C N

R

R

1.12 1.19 1.20

H2O

1.22 1.211.23

HOC

O

NHCN

1.24 1.25

1.2b

Scheme III: Nucleophilic attack of hydroxide to form the cyano hydroxy

lactam23,27

The formation of 1.2 shown in Scheme IV below is also based on the explanation of the

cyano group stabilization as postulated in Scheme III. The hydroxy group in 1.26

should similarly stabilize the cation and result in the formation of 1.2. Attack of

hydroxy anions instead of cyanide ions on the carbonyl carbon atom of the cyanohydrin

1.19 also results in the conversion of dione 1.1 to the dihydroxylactam.27

8

1.2

HOC

O

NHOH

1.28

1.261.19

HOC

O

NH OH

O

HOC

N

HOC O

OH

N

HOC O

OH

HN

H2O

1.27

-

OH-

-

+

Scheme IV: Nucleophilic attack of hydroxide to form the

dihydroxylactam23,25,26,27

9

CHAPTER 2

2. THEORETICAL TOOLS FOR MOLECULAR ORBITAL CALCULATIONS

2.1 Molecular Orbital Theory

Molecular orbital theory is an approach to molecular quantum mechanics which uses

one-electron functions or orbitals to approximate the full wavefunction. A molecular

orbital, (x, y, z), is a function of the cartesian coordinates of a single electron. Its

square, 2(or square modulus | |

2 if is complex) is interpreted as the probability

distribution of the electron in space. To describe the distribution of an electron

completely, the dependence on the spin coordinates , also has to be included. This

coordinate takes on one of two possible values (½) and measures the spin angular

momentum component along the z-axis in units of h/2 .31

2.2 Molecular Mechanics

Molecular mechanics (MM) simulations use the laws of classical physics to predict the

structures and properties of molecules. There are many different molecular mechanics

methods. Each one is characterized by its particular force-field. A force-field

comprises a set of equations defining how the potential energy of a molecule varies with

the locations of its component atoms and a series of atom types, defining the

characteristics of an element within a specific chemical context.32,33

The atom types

describe different characteristics and behaviour for an element depending upon its

environment. For example, a carbon atom in a carbonyl is treated differently than one

bonded to three hydrogens. The atom type depends on hybridization, charge and the

types of the other atoms to which it is bonded. Molecular mechanics calculations don‟t

explicitly treat the electrons in a molecular system. Instead, they perform computations

based upon the interactions among the nuclei. Electronic effects are implicitly included

in force-fields through parameterization. This approximation makes molecular

mechanics computations quite inexpensive computationally, and allows them to be used

for very large systems containing many thousands of atoms. However, it also carries

several limitations as well. The most important is that each force-field achieves only

good results for a limited class of molecules, related to those for which it was

10

parameterized. No force-field can generally be used for all molecular systems of

interest. Neglect of electrons means that molecular mechanics methods cannot treat

chemical problems where electronic effects predominate. For example, they cannot

describe processes which involve bond formation or bond breaking. Molecular

properties which depend on subtle electronic details are also not reproducible by

molecular mechanics methods.34

2.3 Electronic Structure Methods

These methods use the laws of quantum mechanics rather than classical physics as the

basis for their computations. According to quantum mechanics, the energy and other

related properties of a molecule may be obtained by solving the Schrödinger equation:

H = E (2.1)

where, H = Hamiltonian, a differential operator which like the energy in classical

mechanics, is representative of the kinetic and potential energy of the

molecule,

E = numerical energy of the state, and

= corresponding wavefunction for molecular state.

The Hamiltonian used in the Schrödinger equation is that for nuclear motions,

describing the vibrational, rotational and translational states of the nuclei.35

Schrödinger‟s equation for molecular systems can only be solved approximately. Exact

solutions of the Schrödinger equation may only be obtained for the very simplest

molecules (e.g., H2) because of the inter-electronic repulsion terms in the equation,

where the motion of each electron depends on the motion of the other electrons, so

approximate methods have to be used for larger molecules, for example the variation

method.36

The two main classes of electronic structure methods are semi-empirical

methods and ab initio methods.33

Semi-empirical methods use parameters derived from

experimental data or high level ab initio calculations to simplify the computation. An

approximate form of the Schrödinger equation is solved which depends on having

appropriate parameters available for the type of chemical system in question.

11

2.3.1 The Ab Initio Method

The term ab initio is given to computations which are derived directly from theoretical

principles with no inclusion of experimental data. The approximations are usually

mathematical approximations, such as using a simpler functional form for a function or

getting an approximate solution to a differential equation. The square of the

wavefunction 2 is interpreted as the probability density for the electrons within the

system. The first step in simplifying the general molecular problem in quantum mechanics

is in the separation of the nuclear and electronic motions. This is possible because the

nuclear masses are much greater than those of the electrons and, therefore, nuclei move

much more slowly. This separation of the general problem into two parts is called the

adiabatic or Born-Oppenheimer Approximation.37

Thus, the electron distribution within a

molecular system depends on the positions of the nuclei, and not on their velocities.

The advantage of ab initio methods is that they eventually converge to the exact

solution, once all of the approximations are made sufficiently small in magnitude.

However, this convergence is not monotonic. Sometimes, the smallest calculation gives

the best result for a given property.

The disadvantage of ab initio methods is that they are expensive. These methods often

take enormous amounts of computer CPU time, memory and disk space. In practice,

extremely accurate solutions are only obtainable when the molecule contains about half

a dozen electrons or less.

Restricted Hartree Fock (RHF) or Unrestricted Hartree Fock are the two forms of the

wave function that are used in quantum mechanic calculations. The RHF wave function

is used for singlet electronic states, for example, the ground states of stable organic

molecules. The UHF wave function is most often used for multiplicities greater than

singlets.38

The Mller-Plesset second order perturbation theory (MP2) specifies the

calculation of electron correlation energy. The MP2 option can only be applied to

Single Point calculations.39

In general, ab initio calculations give very good qualitative results and can give

increasingly accurate quantitative results as the molecules in question become smaller.31

12

2.3.2 Semi-Empirical

Semi-empirical (SE) calculations are set up with the same general structure as a Hartree

Fock (HF) calculation. Within this framework, certain pieces of information such as

two electron integrals are approximated or completely omitted. In order to correct for

the errors introduced by omitting part of the calculation, the method is parameterized,

by curve fitting a few parameters or numbers in order to give the best possible

agreement with experimental data.40

The advantage of semi-empirical calculations is that they are much faster than the ab

initio calculations. The disadvantage is that the results can be erratic. If the molecule

being computed is similar to molecules in the database used to parameterize the method,

then the results may be very good. If the molecule being computed is significantly

different from anything in the parameterization set, the answers may be very poor.40

Semi-empirical calculations have been very successful in the description of organic

chemistry where there are only a few elements used extensively and the molecules are

of moderate size. However, semi-empirical methods have been devised specifically for

the description of inorganic chemistry as well.40

2.3.3 Density Functional Theory (DFT) Methods40

Density Functional Theory (DFT) is the third class of electronic structure methods that

have recently come into wide use. These methods are similar to the ab initio methods in

many ways. DFT calculations require approximately the same amount of resources as

the Hartree-Fock theory, but they produce results approaching the quality of the MP2

level of theory.

DFT methods include the effects of electron correlation, where electrons in a molecular

system react with each other's motion and attempt to keep out of each other's way. This

is what makes DFT methods more attractive than the expensive ab initio methods.40

DFT methods are based on the theory developed by Hohenberg and Kohn41

in which

they demonstrated that the ground state energy of any molecule can be described in

terms of the total electron density, in other words, each molecule has a unique

functional form which exactly determines the ground state energy and electron density

13

(i.e. geometry) of the molecule.40,42

This system is different to the wave function

approach of ab initio techniques, where the complexity of the wave function increases

by a factor of 3N for an N-electron system (no spin included). For the DFT system, the

complexity of the function is less dependent to the system size since the electron density

has the same number of variables. The aim of DFT methods, therefore, is to design

functions which connect the electron density with energy.43

Kohn and Sham44

were

responsible for the introduction of orbitals which formed the basis for the use of DFT

calculations in computational chemistry.

The advantage of DFT is that only the total density is to be considered and to calculate

the kinetic energy with accuracy, orbitals need to be re-introduced. The disadvantage of

DFT is the derivation of suitable formulae for the exchange-correlation term. DFT

methods, however, have the ability to produce accurate results.42

2.3.4 Basis Sets45

A basis set is a mathematical description of the orbitals within a system used to perform

the theoretical calculation. The wavefunction , can be expanded in terms of a set of

atomic orbitals, in the linear combination of atomic orbitals (LCAO) method, to

give45

:

= c (2.4)

where c = molecular orbital expansion coefficient, and

= basis function of atomic orbital.

The coefficient c is varied to obtain the wavefunction , which will give the lowest

energy in the Schrödinger equation. The more vibrational parameters used to describe

an individual orbital, the lower the energy. However, a situation is reached when the

energy is no longer decreased when the number of vibrational parameters is increased

and then the best single determinant wavefunction is obtained. When this occurs,

changing the wavefunction , by an infinitesimal amount will not alter the energy. The

number and quality of the atomic orbitals determine the quality of the molecular

orbital . If there are many electrons in a molecule then the number of atomic integrals

14

required increases rapidly and can be as many as several million for quite small

molecules. For this reason a fast computer which has a large storage capacity is

essential. The two types of atomic basis functions are Slater-type atomic orbitals (STOs)

and Gaussian-type atomic orbitals (GTOs). The former is not well suited to numerical

work, and their use in practical molecular orbital calculations has been limited. Almost all

modern ab initio calculations employ GTO basis sets. These basis sets, in which each

orbital is made up of a number of Gaussian probability functions, has considerable

advantages over STOs. The Gaussian series of programs deals, as the name implies,

almost exclusively with Gaussian-type orbitals.

2.3.4.1 Minimal Basis Sets45

These contain the minimum number of basis functions needed for each atom. Minimal

basis sets are characterized by fixed-size atomic-type orbitals. Each orbital is

characterized by its coefficient and its exponent. They therefore do not have the

capability to expand or contract because the exponent is fixed.

(i) The STO-3G Basis Set45

The series of minimal basis sets consists of expansions of Slater-type orbitals (STOs).

The STO-3G basis set yields properties that are reasonably close to limiting values and

in view of the relative computational times of the various expansions, it is this level that

has been selected as an optimum compromise for widespread application. Another

possible exception to the use of the three-gaussian expansion as the standard minimal

basis level occurs in the consideration of the properties of weakly-bound complexes

where long-range forces are important.

2.3.4.2 Split Valence Basis Sets45

The way that a basis set can be made larger is to increase the number of basis functions

per atom. Inclusion of two sets of isotropic p-functions in the representation, one tightly

held to the nucleus and the other relatively diffuse, will allow independent variation of

the radial parts of the two sets of p-functions, thus producing more contracted or more

diffuse functions that would be suitable for the descriptions of say, s- and p-systems,

respectively. A basis set formed by doubling all functions in a minimal representation

15

is known as a double-zeta basis, while one in which only the basis functions for the

outer valence shells are doubled, is known as a split-valence basis set.

(i) The 3-21G Basis Set45

The 3-21G basis set defined through the fourth row of periodic table of elements, typify

representations in which two basis functions, instead of one have been allocated to

describe each valence atomic orbital. Except for hydrogen, the 3-21G basis sets are

employed as is, that is, without rescaling of the valence functions to account better for

changes that might occur as a result of molecule formation.

2.3.4.3 Polarised Basis Sets45

While split valence basis sets allow orbitals to change their size, but not their shape,

polarised basis sets remove this limitation by adding orbitals with angular momentum

beyond that which is required for the ground state description of each atom. For

example, polarised basis sets add p-functions to hydrogen atoms, d-functions to the

main groups and f-functions to transition metals.

(i) The 6-31G* Basis Set45

The 6-31G* basis set was originally proposed for first-row atoms and later extended to

second-row elements. The 6-31G* basis set is constructed by the addition of a set of six

second order (d-type) gaussian primitives to the split valence 6-31G basis set

description of each heavy (non-hydrogen) atom.

(ii) The 6-31G** Basis Set45

The basis set described above does not allow for any polarisation of the s orbitals of

either hydrogen or helium atoms. The 6-31G** basis set is identical to 6-31G* except

for the addition of a single set of gaussian p-type functions to each hydrogen and helium

atom.

(iii) The 3-21G* Basis Set45

The 3-21G* basis set for second-row elements are constructed directly from the

corresponding 3-21G representations by the addition of a complete set of six second-

order gaussian primitives. Although the resulting representations contain the same

number of atomic basis functions per second-row atom as the 6-31G* polarisation basis

16

set previously described, these are made up of significantly fewer gaussians (three

instead of six for each inner-shell atomic orbital, and two gaussians instead of three for

the inner part of the valence description).

2.3.4.4 Basis Sets Incorporating Diffuse Functions45

The basis sets that have been discussed thus far are more suitable for molecules in

which electrons are tightly held to the nuclear centers than they are for species with

significant electron density far removed from those centers. Calculations involving

anions pose special problems. Since the electron affinities of the corresponding neutral

molecules are typically quite low, the extra electron in the anion is only weakly bound.

One way to overcome problems associated with anion calculations is to include in the

basis representation one or more sets of highly diffuse functions. These are then able to

describe properly the long-range behavior of molecular orbitals with energies close to

the ionization limit.

(i) The 3-21+G and 3-21+G* Basis Set45

The 3-21+G basis set for the first-row elements and the 3-21+G* basis set for the

second-row are constructed from the underlying 3-21G and 3-21G* representations by

the addition of a single set of diffuse gaussian s- and p-type functions. For first-row

elements with lone pairs, the effects of diffuse and polarisation functions are

complementary to some extent. Hence, the energies of processes involving changes in

the number of lone pairs, for example, protonation, hydrogen bonding, or other

interactions, are improved at diffuse-orbital-augmented levels even when large basis

sets are used.

This basis set produces entry level results and is relatively inexpensive in terms of

computer resources and time. If the system under study involves only C, H, N and O

atoms, the system (with RHF) is ideal for student training. Upgrading to a better basis

set is trivial and one does not loose too much valuable time during your learning curve.

2.3.5 Hartree-Fock Theory46

The most common type of ab initio calculation is the Hartree Fock (HF) calculation in

which the primary approximation is the central field approximation. This means that

the Coulombic electron-electron repulsion is not specifically taken into account.

17

However, its net effect is included in the calculation. This is a variational calculation,

meaning that the approximate energies calculated are all equal to or greater than the

exact energy. Because of the central field approximation, the energies from HF

calculations are always greater than the exact energy and tend to a limiting value called

the Hartree Fock limit. This variational principle leads to the following equations

describing the molecular orbital expansion coefficients, derived by Roothaan and

Hall46

:

01

vi

N

v

viv cSF (2.2)

where, = 1, 2, …, N and cvi = molecular orbital expansion coefficient.

Equation (2.2) can be re-written in matrix form:

FC = SC (2.3)

where F = the Fock matrix,

S = the overlap matrix,

= the diagonal matrix, and

N = one-electron function or basis function.

Equation (2.3) is not linear and therefore must be solved iteratively. The procedure by

which this is carried out is called the self-consistent field (SCF) method.46

Slater and

Gaussian type orbitals are used in these equations. The Hartree Fock equations are

applicable no matter how many electrons there are in the molecule. However, this

theory does not include a full treatment of the effects of electron correlation, that is, the

energy contributions arising from electrons interacting with one another. It is

reasonably good at computing the structures and vibrational frequencies of stable

molecules and some transition-states. As such, it is a good base-level theory.46

The second approximation in HF calculations is that the wave function must be

described by some functional form, which is only known exactly for a few one electron

systems. The functions used most often are linear combinations of Slater-type orbitals

18

(STOs) or Gaussian-type orbitals (GTOs). The wave function is formed from linear

combinations of atomic orbitals or more often from linear combinations of basis

functions. Because of this approximation, most HF calculations give computed energy

greater than the Hartree Fock limit. The exact set of basis functions46

used is often

specified by an abbreviation, such as STO-3G or 6-31g**.

19

CHAPTER 3

3. TRANSITION STRUCTURE MODELING47

A transition structure (TS) is the molecular species that is represented by the top of the

potential energy graph in a simple one dimensional reaction coordinate shown in Figure

3.1. In order to determine the energy barrier to reaction rate, the energy of this

transition-state species is needed. The geometry and energy of a transition structure

include important pieces of information for describing reaction mechanisms.

En

erg

y

Reaction coordinate

Reactants

Products

Transition state

Precomplex

Precomplex

Figure 3.1 Points on a simple reaction coordinate48

A transition structure is defined mathematically as the geometry which has a zero

derivative of energy with respect to moving every one of the nuclear coordinates and

has a positive second derivative of energy of all but one geometric movement which has

a negative curvature.47

This description however, describes many structures other than

a reaction transition, for example an eclipsed conformation or the intermediate point in a

ring flip, a simple rotation of a methyl group or any structure with a higher symmetry

than the ground state of the compound.

It is difficult to predict what a transition structure will look like without the aid of

computer simulation. Such a prediction might be made based on a proposed

mechanism, which may be incorrect. The potential energy surface (PES) around the

transition structure is often much more flat than the surface around a stable geometry,

thus there may be large differences in the transition structure geometry between two

20

seemingly very similar reactions and with very small differences in energy.47

It has

however been possible computationally, to determine transition structures, although it is

not always easy. Experimentally, it has only become possible to examine reaction

mechanisms directly using femtosecond pulsed laser spectroscopy. It will be some time

before these techniques can be applied to all of the compounds that are accessible

computationally. Furthermore, these techniques yield indirect information such as

vibrational information rather than a likely geometry for the transition structure.47

Synthetic approaches to obtain information about transition-states are also limited to

very special cases, such as the static SN2 transition-state 3.1 shown below.49

OMeMeO C

OMeMeO

3.1

An X-ray structure of the above mentioned molecule was reported.49

3.1 Transition-state modeling with empirical force-fields50

The transition-states (TS) involved in a conformational equilibrium can be studied using

the ground-state parameters developed from geometries and heats of formation of stable

molecules. One of the earliest applications of empirical force-fields to organic

chemistry was Westheimer‟s study of rotational barriers in biphenyls, which begun in

the 1940‟s and was reviewed in the 1950‟s.51,52

In the subsequent half-century, there

have been many studies of conformational rate processes in organic systems. Ground-

state parameters are fully appropriate to such studies; transition-states have more torsion

and non-bonded strains than energy minima, but have the same type of bonds.

However, when bonds are being formed or broken, the parameters suitable for ground

states are no longer appropriate.50

Consequently, parameters must be developed to

model partial bonds in a quantitative way when using semi-empirical methods.

Theoretical studies on transition structures of several class of reactions have shown that

21

bond lengths and other geometrical parameters in transition structures have a relatively

narrow range of values. For example, in pericyclic reactions, forming C-C single bonds

generally have bond lengths from 1.95 to 2.28 Ǻ, even though some of these reactions

are very exothermic and others are thermoneutral.53

Radical additions to alkenes have

been studied for a variety of carbon- and oxygen- centred radicals, with constant angles

and bond lengths around 105 ± 3 and 2.25 ± 0.01 Ǻ, respectively.54

Hydroborations of alkenes and alkynes have been studied for a variety of alkylboranes

and substituted ethylenes. Even in the presence of high steric hindrance, the formation

and the breaking up of bond lengths are relatively constant.55

These examples support

one critical procedure often used in simple force-field transition-state modeling, namely

the breaking and forming bonds are either fixed at some lengths, or these values are

treated as energy minima. The energy is actually a maximum for the reaction

coordinate, but the simple expedient of calculating transition-states as minima has been

used in many cases. The TS is a saddle point along the free-energy surface. This saddle

point has a negative curvature in only one direction. The negative force constant

corresponds to motion along the reaction coordinate. All other vibrational motions have

positive force constants exactly like energy minima on potential energy surfaces.

However the negative force constant causes the transition structures to have unique

properties different from force minima.

As mentioned at the beginning of this chapter the energy surface at the TS is often very

flat. This normally causes problems for using SE methods to determine transition-

states.

Due to the structural features and characteristics in the highly strained moieties, the

outer limits of what can be prepared and studied regarding thermodynamic stability and

kinetic reactivity is investigated. Studies of such systems provide an excellent test for

existing chemical theory and thus perhaps furnish the best opportunity for advancing the

frontiers of our chemical knowledge.7 It is therefore likely that SE methods will give

poor results for transition-states involving the cage structure.

22

3.2 Locating minima on the seams of intersecting semi-empirical PES56

Although the word "minima" is used above, it actually implies the lowest maximum on

the energy surface between the product and the reactant.

In recent years, the location of TS‟s has become relatively routine due to improvements

in the optimization algorithms. The TS can be refined to any desired accuracy, if the

energy-generating function is of the ab initio type. However, the practical consideration

usually limits both the size and the level of sophistication. Semi-empirical methods can

be used for somewhat larger systems, but in this case only comparison with experiments

or accurate ab initio calculations can be used to assess the quality of results.

The primary concern in many applications is not in the prediction of absolute values of

activation parameters, but rather on how they vary for closely related systems. There

are two or more reaction pathways that have activation energies which differ by only a

few kcal mol-1

and synthetic sequences are often dependent on these pathways. In such

cases, the desired reaction can often be favoured by a careful selection of substituents at

specific sites in the molecule being studied. According to the influence they have on a

reaction, substituents can be divided into two limiting cases; those of a “structural” or

“steric” nature and those which mainly exert an “electronic” influence. While the latter

requires an explicit description of the electrons in the system, the former can be

modeled by less rigorous theoretical methods, i.e. SE or MM. However, the above

classification of substituents will depend on the given reaction.56

The treatment of a TS as a minimum on the PES is a more fundamental problem with

Houk's approach.56

These directions can in general be written as a linear combination

of internal or cartesian coordinates. Three different strategies can be employed in

transferring the ab initio structure to the force-field model:

(i) The "fixed atom” procedure, where the atoms directly involved in the

reaction are frozen by fixing their cartesian coordinates;

(ii) The “fixed parameter” procedure, where certain internal coordinates are

constrained by assigning large force constraints to these variables; and

23

(iii) The “flexible parameter” procedure, where all atoms are allowed to

move.

As an alternative, the equivalent of a TS in a force-field environment can be defined as

the lowest energy structure linking the reactant and product. When different sets of

parameters are needed for describing the two end points, the TS equivalent is thus the

lowest energy structure on the seam of the intersecting PES‟s. The advantage of the

current strategy over Houk‟s TS modeling, is that only information regarding the two

minima (reactant and product) on the PES is needed, and such data are in principle

accessible by experiments. The disadvantage is that the functional form of the energy

must be reasonably accurate over a wider range of geometries than just near the

"minima".

SE methods were initially employed in this study for the determination of transition

structures. It was found that the method indeed produced poor quality results, and in

many cases the correct transition structures could not be found. It was therefore decided

to use ab initio techniques for the determination of the required transition-states.

3.3 Transition-structure modeling of a PCU Cage Lactam using ab initio

methods

The TS algorithm uses a combination of Rational Functional Optimization (RFO) and

linear search step to search for the lowest maximum on the energy surface between the

reactant and the product. A mathematical algorithm by default uses a crude semi-

empirical (SE) guess (INDO guess is used for the first-row systems, CNDO for the

second-row, and Hückel for the third-row and beyond)57

for the initial start structure to

the solution of the transition-state wave function. If the starting structure is too far from

the real maximum on the energy surface, the search algorithm would not find the correct

transition structure within the multitude of local maxima.

In order to obtain a better guess for the solution to the wave function, one could use

either of two methods:

(i) carry out a Single Point (SP) calculation of the starting structure at the

same level of theory using the same basis set, followed by an additional

24

step in the calculation, with the option to read the guess (guess = read)

from the calculation done (obtained from the checkpoint file) at the

required level and basis set or

(ii) use the option “CALCFC” where the force constant is calculated at the

required level/basis set and used to start the solution to the wave

function. The second option is considerably more expensive in terms of

resources and time, since the “CALCFC” option does the same

calculation as required for a frequency calculation. (see Chapter 4 for a

discussion on CALCFC).57

A third method is the QST2 and QST3 methods in Gaussian which has the facility for

automatically generating a starting structure for a transition-state optimization based

upon the reactants and products that the transition-state connects,58

known as the

Synchronous Transit-Guided Quasi Newton (STQN) method. This method uses a

quadratic synchronous transit approach to get closer to the quadratic region of the

transition-state, and uses a quasi-Newton or eigenvector-following algorithm to

complete the optimization.57

QST2 requires two molecule specifications, i.e., the

reactants and products. QST3 requires three molecule specifications, that is, the

reactants, the products and an initial structure for the transition-state, respectively. The

QST2 and QST3 methods were utilized in this study, but it did not yield favourable

results.

A fourth option is to use the “CALCALL” option in combination with the transition-

state optimization. During this calculation, the force constant will be calculated for

each optimization step. This option is very expensive and is only used as a last resort

when the methods above do not show positive results.

In this study, the TS for a PCU cage lactam were found by locating maxima on the

potential energy surfaces using Restricted Hartree-Fock theory and the 3-21+G* basis

set. For each TS (see Chapter 5 for the mechanistic pathway) a SCAN calculation (see

Chapter 4 for computational details) was performed to establish the maxima. The final

structure corresponds to a minimum on the potential energy surface, or saddle point. In

order to determine the nature of the stationary point found, a frequency calculation was

25

performed. The frequency output file has information that is critical in characterizing

the stationary point, namely, the number of imaginary frequencies and the normal mode

corresponding to the imaginary frequencies. Imaginary frequencies are listed in the

output file as negative numbers. By definition, a structure which has n imaginary

frequencies is an nth

order saddle point. Thus transition structures are usually

characterized by one imaginary frequency since they are first-order saddle points.59

The

movement of atoms associated with the imaginary frequency should follow the atoms

on the reaction coordinate between the reactant and product. Any reaction profile will

have only one transition-state. Although many intermediate transition structures on the

reaction profile might exist, only one of them will be the rate-determining step. That

transition structure is defined as the transition-state for the reaction.

26

CHAPTER 4

4. COMPUTATIONAL DETAILS EMPLOYED

This study was carried out on a series of related molecules using the GAUSSIAN 9860

program implemented on a DEC Alpha DS20 workstation with two CPU‟s and a

Pentium II desktop computer. A true 64 bit operating system was implemented on the

DEC Alpha workstation with a parallelized version of GAUSSIAN 98 program.

4.1 The GAUSSIAN 98 Program

GAUSSIAN 98 (G98) is one of the series of electronic structure computer programs

which began with GAUSSIAN 70, GAUSSIAN 92 and GAUSSIAN 94. GAUSSIAN

03 is the latest program which was released in April 2003.

The GAUSSIAN programs are general-purpose programs capable of performing ab-

initio Hartree-Fock (HF) molecular orbital calculations based on the linear combination

of atomic orbitals (LCAO) approach. As the name implies, the program deals mainly

with Gaussian-type orbitals, which has been described in Chapter 2. However new

methods have been added to G98 so as to improve optimization procedures for

transition-state calculations.

In addition, G98 can compute energies, molecular structures, vibrational frequencies

and numerous other molecular properties for systems in the gas phase and in solution,

including the ground state and excited states.

The input section to the GAUSSIAN programs consists of the molecular charge and the

multiplicity, the symbols of the constituent atoms and a definition of the molecular

structure, either in the form of cartesian coordinates or the Z-matrix notation, which

defines the molecular geometry in terms of bond lengths, bond angles and dihedral

angles. The task to be performed, i.e. whether a single-point calculation, geometry

optimization or frequency calculation, must also be specified, together with the

appropriate basis set and the level of theory.

The 3-D structures on the CD accompanying this thesis are written in the Gaussian input

file format (gjf). The geometries of the structures can be viewed by using the Gausview

27

program or the freeware (Molekel) program. The installation files for Molekel can be

downloaded from the site: www.cscs.ch/molekel

4.2 The GaussView Program61

GaussView is a Graphical User Interface (GUI) program designed to simplify and

extend the use of the Gaussian 98 program. In this study, Gaussview was used to build

and edit molecules, set up and submit Gaussian jobs, and to display and use the results

from the Gaussian jobs. However, GaussView is not directly integrated into the

Gaussian program system, but acts as a front-end/back-end processor to facilitate its use

on a desktop computer workstation. GaussView was also used to verify the animation

of atoms associated with the negative eigenvalue of the different transition-states.

4.3 The SCAN Calculation

The scan option was exclusively used as an aid to finding an approximate starting

structure for a normal transition-state optimization. A relaxed SCAN calculation

involved changing of bond length from reactants to products, in a step-wise manner.

The only constraint in this calculation is the required reaction coordinate (i.e. bond

length, angle or the dihedral angles). The rest of the molecule is then optimized to find

the lowest possible structure and energy, subject to the imposed constraints, after which

the reaction coordinate is modified by a prescribed value and in the next step the

procedure is repeated. In this study only relaxed SCAN calculations were used. The

energy of each step was plotted against the reaction coordinate. By inspecting the

different structures at each step of the scan job, one could follow the course of the

reaction. The approximate starting structure for a full (non-restrained) transition-state

optimization was obtained by manually extracting the coordinates of the structure

closest to the maxima on the energy vs. reaction coordinate plot. The TS was verified

by performing a frequency (FREQ) calculation. A frequency calculation produces only

one negative eigenvalue, which is usually associated with the movement of atoms

involved in either bond breaking or bond formation.

http://www.cscs.ch/molekel

28

4.3.1 Commands used during a SCAN or a TS Search60

(i) GDIIS

Specified the use of the modified GDIIS algorithm, recommended for use with

larger systems, tight optimizations and molecules with flat potential energy

surfaces. It is the default for semi-empirical calculations. This command makes

use of a smaller step-size down the potential energy valley.60

(ii) MODREDUNDANT or ModRed

Used in geometry optimization, e.g. the bond length to be scanned. The specific

coordinates that are to be constraint (Modified Redundant coordinates = ModRed) is

specified below the Cartesian coordinates.60

(iii) TS

Used in a search to request the optimization to use a mathematical search algorithm

which aims to find a local maxima on the potential energy surface (i.e. a transition-

state) rather than a local minimum.60

(iv) NOEIGENTEST

The default transition-state search in G98 makes use of the EigenTest. If only one

imaginary frequency is found, the calculation continues to find the transition-state

associated with this negative eigenvalue. If more than one imaginary frequency

exists, the default routine is to terminate the calculations. Since it is practically

almost impossible to find a starting structure for a TS with one and only one

negative eigenvalue, the default TS calculation terminates very often. In order to

overcome this oversensitive search criterion, one uses the "NoEigenTest" option

which overrides the default search criteria in G98.60

(v) CALCFC

Specified the force constants be computed at the first point using the current method

(available for the HF, MP2, CASSCF, DFT, and semi-empirical methods only). By

default Gaussian uses a MNDO (semi-empirical) guess for the solution to the wave

function of the specified system. The optimization uses this guess as starting point

29

where, after the ab initio calculation is “built” on this starting point. Since the

MNDO guess is based on a rather crude or inaccurate method, the calculation could

sometimes follow a wrong solution for the wave function. One observes this by

inspecting the geometry of the structure produced by the optimization, there are

basically two choices: (a) start with a better structure, i.e., a structure that was

optimized at a lower level of theory or (b) if a better starting structure was already

used, use the CalcFc option.3,60

4.4 Calculation Details

In this study the procedure for all structures was the structures in HyperChem Version

5.62

In order to remove any van der Waals contacts or overlap, an energy minimization

was performed with ChemOffice,63

using a molecular mechanics force-field. The final

structures were saved as input files for GAUSSIAN 9860

(G98W). A low level (STO-

3G) ab initio (full geometry optimization) calculation was carried out on the

unconstrained molecule. The (OPT) keyword requests that a geometry optimization be

performed. The geometry is adjusted according to a mathematical algorithm to follow

the energy surface “down hill” until a stationary point on the potential energy surface is

found. Note that the algorithm by nature would not overcome local minima and special

techniques such as automatic or manual conformational searches or molecular

dynamics64,65,66

should be employed to overcome, mainly, rotational energy barriers.

This is more problematic in flexible molecules such as peptides.

For the Hartree-Fock, DFT and semi-empirical methods, the Berny algorithm is the

default algorithm for minimizations to a local minimum and optimizations to transition-

states and higher order saddle points.57

The purpose of a geometry optimization is to

locate the lowest energy of the molecular structure that is in close proximity to the

specified starting structure. The output structure of the optimization was submitted on a

DEC Alpha workstation using the RHF/3-21+G* level of theory. A SCAN calculation

was performed to locate the maxima on the PES. The starting structure for the

transition-state (TS) calculation was obtained by manually extracting the coordinates of

the structure that correspond to the maxima. Once a TS was obtained a frequency

calculation was carried out to verify that there is only one negative eigenvalue.

30

CHAPTER 5

5. RESULTS AND DISCUSSION

5.1 Introduction

The purpose of this study is to utilize computational techniques in the determination of

the proposed mechanistic pathways, for the one-pot conversion of pentacyclo-undecane

(PCU) dione 5.1 to pentacyclo-undecane cage lactam 5.2.23,25

OO

NaCN

H2O

OH

C O

NHHO

5.1 5.2

This chapter focuses on the calculation results obtained for the proposed mechanistic

pathway as illustrated in Figure 5. 1 (see Page 31). The basis set incorporating diffuse

functions, that is, 3-21+G* was used in this study as discussed in Chapter 2. The

mechanism, which was one of two possible pathways that was proposed23,25,26,27

is

based on basic chemical principles and intuition and was discussed in Chapter 1. In this

study, the pathway proposed above was used as basis for the calculation of the reaction

profile. Based on the observations made during this investigation (i.e., a starting

structure optimized to a different intermediate or transition structure) the proposed

pathway was also modified. The energies for the calculated mechanism proposed in this

study are depicted in the form of a reaction profile (Figure 5.2 Page 32).

The reaction profile was investigated by first calculating the geometries and energies of

the minima on the energy surface (Figure 5.2). Since the cage is very rigid, very few

problems with conformational isomers of higher energies, were experienced.

The structures and energies of the corresponding TS's were then calculated. The

procedure for locating the TS's is described in Chapter 3, Section 3.3.

31

5.1

NaCN

H2O

5.3.1

H2O

5.4

-OH

+ NaOH

5.9

5.2

5.5 5.6 5.7.1

5.10 5.11

N

OH

OH

C

5.13

O

O O

O-

CN

O

CN

OH

O

HO

CN

O

HO

CN

O

HO

HO

OH

CN

OH

HO

HN

OH

C

OHO

HN

O

OH

C

HOHN

O

OH

C

HO

5.12

HN

O

OH

C

HO

CN

OH

Figure 5. 1 Modified23,25,26,27

mechanism for the conversion of the dione 5.1 to

the lactam 5.2.

32

5.1

5.2

5.3.1

5.4

5.5

5.7.1

5.9

5.12

5.13

-100

-50

0

50

100

150

200

250

300

Reaction Co-ordinate

5.105.65.11

O

OO

CN

OH

CN

O

HO

CN

O

HO N

OH

OH

C

HO

OH

CN

OH

HO

HN

OH

C

OHO

HN

O

OH

C

HO

HN

O

OH

C

HO

HN

O

OH

C

HO

CN

OH

OHO

O-

CN

O

Rel

ati

ve

ener

gy

(k

cal

mo

l-1)

Figure 5.2 Calculated reaction profile for the proposed mechanism.

The cartesian coordinates of all the 3D structures presented in this Chapter are included on the CD accompanying this Thesis.

33

5.2 Local minima on the energy profile

Structures 5.1, 5.4, 5.6, 5.9, 5.11, and 5.2 shown below are stationary points classified

as local minima on the energy profile of the reaction.

5.1

O

O

5.4

O

CN

OH

5.6

CN

O

HO

5.9

N

OH

OH

C

HO

5.11 5.2

HN

OH

C

OHOHN

O

OH

C

HO

An energy minimization was performed for each of the above structures to remove

any Van der Waals contacts or bond overlap. The calculated energies for the above

structures are presented in the Table 5.1. Note that the only rotational flexibility in

these structures are the C-OH bonds illustrated above. The corresponding bonds were

rotated at angles of 30º intervals and re-optimized to ensure the lowest possible

isomer was obtained.

Table 5.1 Calculated energies of the local minima.

Relative energiesa

Structure numberb

STO-3G/Hartrees 3-21+G*/Hartrees 3-21+G*/kcal mol-1

5.1 -565.0296 -568.9543 0

5.4 -656.7586 -661.3513 27.66

5.6 -656.8147 -661.3657 18.66

5.9 -731.7744 -731.9821 19.79

5.11 -731.8214 -737.0049 6.19

5.2 -771.8263 -737.0314 -10.46

aRelative energies are expressed in Hartrees and kcal mol

-1, performed at the HF level using the STO-

3G basis set, followed by a higher 3-21+G* level of theory.

bStructure number as per proposed reaction mechanism shown in Figure 5.1.

34

From the results presented in Table 5.1, it is evident that the higher level basis set

produces a significantly lower energy value. (Note that energies obtained with

different basis sets cannot be directly compared). In addition, when the reaction

profile as shown in Figure 5.2, was plotted, it was also evident that the energy values

(heats of formation) confirm that structures 5.1, 5.4, 5.6, 5.9, 5.11, and 5.2 are indeed

minima.

5.3 The Transition Structures (TS)

Structures 5.3.1, 5.5, 5.7.1, 5.10, 5.12 and 5.13 shown in Figure 5.1 are characterized

as the following transition-state structures.

5.3.1

O-

CN

O

5.5

CN

O

HO

5.7.1

CN

OH

O

HO

5.10

OH

CN

OH

HO

5.12

HN

O

OH

C

HO

5.13

HN

O

OH

C

HO

The cartesian coordinates of all the 3-D structures presented in this Chapter are

contained on the CD accompanying this Thesis. Please refer to Chapter 3 for a

discussion on the techniques used to determine the transition-states below.

An explanation of the different types of SCAN calculations used in the route section

for the location of the various transition structures is given in Chapter 4. The

calculated energies for the above structures are presented in the Table 5.2.

35

Table 5.2 Calculated energies of the transition structures.

Relative energiesa

Structure numberb

3-21+G*/Hartrees 3-21+G*/kcal mol-1

5.3.1 -660.7663 127.39

5.3.2 -736.9142 63.11

5.5 -661.2569 86.90

5.7.1 -736.3609 188.43

5.7.2 -812.5102 77.74

5.10 -736.8741 88.27

5.12 -736.8873 79.95

5.13 -736.8880 79.55

aRelative energies are expressed in Hartrees and kcal mol

-1, performed at the HF level using the 3-

21+G* level of theory.

bStructure number as per proposed reaction mechanism shown in Figure 5.1.

In the discussion of the results for each of the transition-states, the three dimensional

(3-D) structures have been referred to as Scan start or Scan end. Scan start implies

the starting structure that was submitted for the calculation. Scan end refers to the

corresponding structure that was obtained at the end of the scan calculation. By

inspecting the different structures at each step of the scan job, one could follow the

reaction profile and by plotting the corresponding energies vs. the reaction coordinate,

one can obtain an approximate indication of the transition structure involved. This

approximate starting structure for a full (non-restrained) transition-state search was

obtained from the SCAN calculation by manual isolation of the coordinates of the

structure closest to the maxima on the reaction profile (see Figure 5.3).

The same basic computational methods used for the calculation of the local minima

energies were utilized in locating the geometries of the transition-state structures. The

only difference is that the last part of the procedure made use of a transition-state

optimization during a scan close to the maxima associated with the corresponding TS.

The transition structure that was obtained is referred to TS end. A summary of the

results obtained for each of the transition-state structures follows.

Note that the Gaussian 98 frequency output files of the different transition-states are

available on the CD attached to this thesis. Molekel (freeware) at the site:

36

www.cscs.ch/molekel can also be used to view the frequency output files, in

particular the vibrations associated with the negative eigenvalue.

5.3.1 Transition Structure 5.3.1

A constrained optimized structure (C9-C13, fixed at 1.7 Å) was used as input for a

relaxed SCAN calculation. The three dimensional (3-D) input structure for the

relaxed SCAN calculation is represented below.

5.3.1 (Scan start)

It is clear from the geometry of the structure above that the structure would be close to

the maxima on the energy profile or perhaps closer to the formation of the

intermediates 5.4 or 5.6 (see Figure 5.2). Note the carbonyl carbon (C5) is bending

out of plane, starting to become sp3 hybridised. The reaction coordinate C9 and C13

was scanned from 1.7 Å to 2.2 Å since the TS involved the formation of the bond

between atoms C9 and C13. The output of the Scan optimization is shown below as

5.3.1 (Scan end).

http://www.cscs.ch/molekel

37

5.3.1 (Scan end)

On closer inspection of the Scan end file, it is clear that, as the reaction coordinate

between atoms C9 and C13 increased, the CN group moved away from the cage, and

the distance between atoms C5 and O15 increased accordingly. The carbonyl carbon

(C5) is again sp2 hybridised. The reaction profile of the step-wise increase in bond

length between atoms C9 and C13 is graphically presented in Figure 5.3.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

1.6 1.8 2 2.2

Reaction Coordinate/Å

Rel

ati

ve

En

erg

y/k

cal

mo

l-1

Figure 5.3 Graphical representation of energy vs reaction coordinate for

structure 5.3.1.

Figure 5.3 shows that a minimum energy value occurs at 1.9 Å and a maximum

energy at 2.1 Å. Closer examination of the structure at the maxima of 1.8 Å and the

structure at the minima of 1.9 Å suggests that it is due to the rotation of the cyano CN

group (C13-N14), that is, the cyano group moving from the front of the cage to the

38

back, as shown in the 3-D structures below. This phenomenon is therefore not likely

to be associated with the required transition structure - one would rather expect bond

formation/dissociation between C9 and C13.

The coordinates of the structure closest to the second maxima (2.1 Å) was manually

extracted from the Scan output file. This geometry of the structure was found to be

close to the expected TS. Thus a TS search was carried out using the structure at 2.1

Å as approximate starting structure for a full transition-state optimization. The 3-D

TS optimization is shown below.

5.3.1 TS end

The TS calculation was verified by performing a frequency (FREQ) calculation

resulting in ONE negative eigenvalue only. The FREQ calculation was viewed using

the GaussView61

program, enabling the vibration mode, associated with the negative

eigenvalue, so that the bond formation between the cyano group (C13-N14) and C9 is

clearly visualized. The vibration associated with the imaginary frequency shows the

39

cyano group (C13) moving towards the cage to form a bond with C9. It is also clear

that the carbonyl carbon (C9) is converted to a sp3 carbon while O15 is moving

towards C5 as the nucleophile C13 is approaching the carbonyl carbon C9.

5.3.2 Transition Structure 5.5

Finding transition structure 5.5, (see Figure 5.2), involved monitoring the

intramolecular transfer of the hydrogen atom (H26) between the two oxygen atoms

(O12 and O15). Shown below is the 3-D structure (5.5-Scan start) which was used

as the starting structure for the relaxed scan.

5.5 (Scan start)

The bond was scanned from 2.2 Å to 1.4 Å. The output 3-D structure 5.5 (Scan end)

is shown below.

40

5.5 (Scan end)

It is clear that the hydrogen (H26) is transferred during the Scan calculation. The

structure 5.5 (Scan end), above, when compared to the 5.5 (Scan start) shows that

the atoms C9-C13-N14 keep a linear bond as expected. Atoms C5 and O15 forms a

bond as the distance between atoms O12 and H26 decreases as a result of the H-

transfer. Atom H26 orientates itself between atoms O12 and O15. The scan is

graphically depicted below.

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

1.2 1.4 1.6 1.8 2 2.2

Reaction Coordinate/Å

Rel

ati

ve

En

ergy/k

cal

mol

-1

Figure 5.4 Graphical representation of energy vs. reaction coordinate for

structure 5.5.

The corresponding structure closest to the maximum in Figure 5.4 is at 1.6 Å. The

structure at this bond length was manually extracted from the scan output file and

41

submitted as input structure for a TS optimization. The resultant TS structure that

was obtained at the end of the TS optimization is represented below.

5.5 TS end

The TS structure was verified to be correct since the FREQ calculation produced only

one negative eigenvalue and the movement of atoms associated with the negative

eigenvalue correspond to the expected movement of atoms on the reaction profile.

This movement includes transfer of atom H26 between atoms O15 and O12 and bond

formation/dissociation between C5-O15 as discussed above.

5.3.3 Transition Structure 5.7.1

The transition structure depicted as structure 5.7.1 was complex and difficult to find

as will be described next.

In structure 5.7.1 the calculations involved monitoring the progress of the hydroxyl

group (O27-H28) attaching to the cage and the breaking of the C9-O15 (ether/acetal)

bond.

42

5.7.1 (Scan start)

The graphical presentation of the relaxed scan, that is, the decrease of the reaction

coordinate as the hydroxyl group (O27-H28) attaches to C9 from 2.4 Å to 1.3 Å is

shown below.

-20.0

-10.0

0.0

10.0

20.0

30.0

40.0

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Reaction Coordinate/Å

Rel

ati

ve

En

erg

y/k

cal

mo

l-1

Figure 5.5 Graphical representation of energy vs. reaction coordinate for

structure 5.7.1.

This transition structure is also an example of a case for which the graph exhibits a

maximum, but is not necessarily indicative of the required transition-state. The

explanation of how the "transition-state" was found follows. The maximum in Figure

5.5 is at 1.8 Å. Thus the transition-state optimization for structure 5.7.1 was carried

out using the structure closest to this maximum bond length (1.8 Å). The 3-D input

structure (5.7.1 TS1 start) which was used for the transition structure optimization

43

and the corresponding 3-D non-restricted output structure (5.7.1 TS1 end) that was

obtained are shown below.

The input structure, 5.7.1 TS1 start, had the hydro