Adhesion between solid bodies plays a prominent role in a wide variety of situations ranging from tribological applications to dust coagulation initiating the formation of planets. It can be due to various reasons like capillary, electrostatic, van der Waals, and hydrophobic forces. Among these, adhesion due to van der Waals force| which has its origin in permanent or instantaneous electric dipoles present in all atoms and molecules|is of special significance as it is present in all cases. Computational studies on adhesion due to van der Waals force commonly assume it as a surface force due to its short effective range, which is about a few tens of nanometers, in comparison to the length-scales commonly encountered. However, such restrictions are often violated in various important problems. For example, the characteristic dimensions of asperities| which are the smallest roughness elements interacting to cause friction and wear| are usually of nanometer length-scale. In addition, the assumptions inherent in development of surface force model are exact only when the deformations are small. In all such situations, the van der Waals force must be assumed as distributed over the volume. In this work, a computational model is developed by incorporating van der Waals force and short-range repulsion (steric repulsion or Pauli repulsion) as body forces distributed over the volume in a large deformation, static/transient, finite element framework. First the development of the general formulation is discussed, and then it is specialized for various considerations like handling symmetry and interaction between an elastic body and a rigid half-space, which offer significant computational advantages over the general formulation. The applicability of the model is illustrated by using a number of benchmark and practical problems. The comparison of the analysis results and well-established analytical models are provided, which validates our method. As a specific example, the smooth change of interaction force from a thin-rod model to a at-plate model on increasing the cross-sectional areas of two interacting elastic rods is demonstrated. The impact of elastic bodies in presence adhesion, and the associated energy loss is an important concern in studies regarding the origin of friction. Therefore, adhesive impact of elastic rods and spheres is studied using our formulation. Emphasis of the study is on finding the apparent energy loss during impact, which represents the part of energy lost to elastic stress waves remaining in the body after the impact, and hence not available for rebound motion. In case of impact of elastic rods on a rigid half-space, it is shown that the apparent energy loss is a unique function of the tensile strain energy developed in the rod due to van der Waals attraction. A one-dimensional model is developed for this case to determine the energy loss based on the specified problem parameters, which can be used to predict practically relevant phenomena like capture. In case of impact of elastic spheres, which is often correlated with asperity interactions, the energy loss is found to be significant only if adhesion-induced instabilities occur. The behavior shown by rods and spheres are probably at the two extremes with regards to energy loss during impact of elastic bodies in presence of adhesion. Practical use of the formulation is demonstrated by applying it to the study of amplitude variation and phase shifts in tapping-mode atomic force microscopy. Specifically, the advantage of operating the AFM cantilever just below its natural frequency as compared to operating it just above the natural frequency is demonstrated. Bistable behavior, which is the coexistence of two stable vibration modes under exactly same operating conditions, is shown to be severe when the driving frequency is higher than the natural frequency of AFM cantilever even in the absence of adhesion, which can result in spurious contrast-reversal artifacts during imaging. The hysteresis loop associated with the bistable behavior may lead to erroneous conclusions regarding presence of adhesion. Since this model overcomes the limitations of lumped parameter models and the computational models based on surface force approximation, the results can be used for much more realistic interpretation of experimental data. Computational framework developed in this study achieves the capability for analysis of adhesive contact problems directly from van der Waals interaction and steric repulsion. Such a model can be used for revisiting the fundamental problems in contact mechanics, as well as for providing better insights into experimental observations.

The importance of weak interactions between molecules to life and all parts of science and engineering is unquestionable and there have been an enormous interest in such interactions. Among all the weak interactions, hydrogen bonding is the most popular and it has enjoyed the most attention of the scientific community. Halogen bonding is gaining more popularity in the recent time, as its importance to biological molecules and crystal engineering has been recognized. In this work, a Pulsed Nozzle Fourier Transform Microwave spectrometer has been used to study the rotational spectra of molecules and hydrogen bonded complexes. Structural information is obtained from the rotational spectra. Ab initio electronic structure, Natural Bond Orbital (NBO) and Atoms in Molecules (AIM) theoretical methods have been used to characterize the weak intermolecular interactions, including hydrogen bonding, halogen bonding and lithium bonding. In Chapter I, introduction to weak interaction is discussed. A brief introduction of different experimental and theoretical methods is presented. Chapter II discusses in detail about the different methods used to investigate weak interaction, both experimentally and theoretically, in this work. In our lab, we use Pulsed Nozzle Fourier Transform Microwave spectrometer to determine the complexes spectra and structures. We generate MW radiation with the help of electronic devices and use Balle-Flygare cavity where molecular interaction takes place. We inject the sample inside the cavity in form of supersonic molecular beam through a pulsed nozzle, parallel to MW radiation. The detailed instrumental discussion about MW spectrometer has been done in this Chapter. We extensively use theoretical methods to probe weak bonding and characterize them. Ab initio and DFT calculations are used to optimize the structure of the complexes and predict their rotational spectra. Atoms in Molecules theory and Natural Bond Orbital theory are then used with the ab initio wave functions to understand the weak interactions in depth. Discussion about these methods and software used for the analysis will also be discussed. In Chapter III, rotational spectrum of Hexafluoroisopropanol (HFIP) monomer is presented. HFIP is an interesting molecule as it offers many possibilities as hydrogen bond donor and acceptor. It has the OH group which can both accept/donate a hydrogen bond and in addition it has a very acidic CH group. It is the only solvent that can dissolve polyethylene terephthalate, a normally difficult-to-dissolve polymer, and clearly it has unique interactions with this difficult to solve polymer. We have recorded and fitted rotational spectra of five different isotopologues of HFIP which helped us in determining its accurate structure. Though, it can exist in synclinical and antiperiplanar conformers, only the later has been detected in our molecular beam spectrometer. This happens to be the global minimum structure of HFIP. Combination of experimental observations and ab initio calculations provided many evidences which confirmed the presence of antiperiplanar conformer, experimentally. Since, the rotational constants for both conformers were very close, it was always challenging to pick up one conformer as experimentally observed structure. A prototype molecule, hexafluoroisobutene (HFIB) shows doubling of rotational transitions due to tunnelling/counter rotation of the two CF3 groups through a small barrier. Interestingly, such motion has no barrier in HFIP and hence no splitting in transitions was observed. Potential energy surface calculated for counter-rotation of the two CF3 groups is consistent with this observation. This barrier is different from eclipsed-staggered exchange barrier, observed by 60 counter rotation of both terminal CF3 groups, for which the barrier height is very large and tunnelling cannot occur. The origin/lack of the small barrier in HFIB/HFIP has been explored using Natural Bond Orbital (NBO) method which helped in understanding intramolecular bonding in these molecules. Along with HFIB, other prototype molecules were also considered for the analysis e.g. hexafluoroacetone, hexafluoroacetone imine, hexafluoroisobutane, hexafluoroisopropylamine. In the last section of this Chapter, we have discussed the generalized behaviour of molecules which have CF3-C-CF3 groups. In Chapter IV, rotational spectrum of HFIP•••H2O complex is presented. Aqueous solution of HFIP stabilizes α-helical structure of protein, a unique property of this solvent. The main objective of this Chapter is understanding the interaction between HFIP and H2O. Microwave spectrum of HFIP•••H2O was predicted and recorded. Three isotopologues were investigated. Though, this complex could in principle have several structural conformers, detailed ab initio calculations predicted two conformers and only one was observed. Though, the rotational constants for both structures were somewhat similar, lack of a dipole transitions, larger intensity of b-dipole transitions over c-dipole transitions and isotopic substitution analysis positively confirm the structure in which HFIP acts as the hydrogen bond donor. The linear O-H•••O hydrogen bond in HFIP-H2O complex is significantly stronger than that in water dimer with the H•••O distance of 1.8 Å. The other structure for this complex, not found in experiment is cyclic with both C-H•••O and O-H•••O hydrogen bonds, both of which are bent with H•••O distances in the range 2.2-2.3 Å. Both AIM and NBO calculations have been used to characterize the hydrogen bond in this complex. In Chapter V, a comprehensive study on hydrogen bonding, chlorine bonding and lithium bonding have been done. A typical hydrogen bonded complex can be represented as A•••H-D, where A is the acceptor unit and H-D is the hydrogen bond donor unit. Many examples are known in literature, both experimentally and theoretically, in which the A-H-D bond angles are not linear. Deviation from linearity also results in the increase in A•••H bond lengths, as noted above for the two structures of HFIP•••H2O complex. Though this has been known for long, the distance between A and D being less than the sum of their van der Waals ‘radii’ is still used as a criterion for hydrogen bonding by many. Our group has recently shown the inappropriateness of van der Waals ‘radii’ and defined hydrogen bond ‘radii’ for various donors, DH and A. A strong correlation of DH hydrogen bond ‘radii’ with the dipole moment was noted. In this Chapter, we explored in detail the angular dependence of hydrogen bond ‘radii’. Electron density topology around DH (D = F, Cl and OH) has been analyzed in detail and shown to be elliptical. For these molecules, the two constants for H atom treated as an ellipse have been determined. It is hoped that these two constants will be used widely in analyzing and interpreting H•••A distances, as a function of D-H•••A angles, rather than one ‘radius’ for H and acceptor atoms. In Chapter VI, Detailed analysis and comparisons among hydrogen bond, chlorine bond and lithium bond, have been done. Hydrogen can be placed in group 1 as well as group 17 of the periodic table. Naturally, lithium bonding and halogen bonding have been proposed and investigated. There have been numerous investigations on the nature of hydrogen bonding and the physical forces contributing to it. In this Chapter, a total of one hundred complexes having H/Cl/Li bonding have been investigated using ab initio, AIM and NBO theoretical methods. Various criteria proposed in the literature have been examined. A new criterion has been proposed for the characterization of closed shell (ionic/electrostatic) and open shell (covalent) interactions. It has been well known that the D-H bond weakens on the D-H•••A hydrogen bond formation and H•••A bond acquires a fractional covalency. This Chapter shows that for D-Li•••A complexes, the ionicity in D-Li is reduced as the Li•••A bond is formed This comprehensive investigation of H/Cl/Li bonding has led us to propose a conservation of bond order, considering both ionic and covalent contributions to both D-X and X•••A bonds, where DX is the X-bond donor and A is the acceptor with X = H/Cl/Li. Hydrogen bond is well understood and its definition has been recently revised [Arunan et al. Pure Appl. Chem., Vol. 83, pp. 1619–1636, 2011]. It states “The X–H•••Y hydrogen bond angle tends toward 180° and should preferably be above 110°”. Using AIM theory and other methods, this fact is examined and presented in Appendix A. In second part of appendix A, a discussion about calling H3¯ complex as trihydrogen bond and its comparison with FHF¯ complex, is presented. In Appendix B, there is tentative prediction and discussion about the HFIP dimer. Condense phase studies show that HFIP have strong aggregation power to form dimer, trimer etc. During, HFIP monomer study, we have unassigned lines which are suspected to be from HFIP dimer. These are tabulated in the Appendix B as well.

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This thesis titled, “Nature of Local Interactions at cisPro-Aro Peptide Sequences in Proteins: Evidences for van der Waals type Interactions. Design and Synthesis of Novel Covalent Surrogates for the Peptide Hydrogen Bond”, describes two important studies. The first is to gain a thorough understanding of the nature of interactions that govern cisPro stability at Pro-Aro sequences, which described in the first four chapters. The final chapter describes the synthesis of novel 4-carbon covalent surrogates for the peptide H-bonding interaction. Chapter 1: Local Interactions Governing cisPro Stability: Refining the Model Peptides Chapter 1 Section A: Understanding the role of inter-side chain CH•••Aro interaction in cis-trans isomerization at Pro-Aro and Aro-Pro Sequences. This chapter is divided into two sections. In the first section an exhaustive overview of earlier investigations into the nature of local interactions at Xaa-cisPro-Aro and Aro-cisPro-Xaa peptide sequences, by various groups, are discussed. Most studies have found evidence for the close assemblage between side chains of residues flanking cisPro motifs, when at least one of them is an aromatic group. An electronic C-H•••π nature has been proposed for these assemblies and they are proposed to influence the cisPro stability. We highlight those features in these studies that indicate that these interactions are not always electronically tunable, are insensitive to presence of strong chaotropes in the solvent and occur at protein sequences lacking Pro or cisPro; all of which contradict the electronic C-H•••π model for these inter-side chain assemblages and their perceived influence on cisPro stability. Chapter 1 Section B: Investigation of the Nature of H Xaa•••Aro interaction at Xaa-Pro-Pro-Phe-sequences In Section B, we design and synthesize Pro-Aro containing short peptide models to investigate the nature of local C-H•••Aro interactions in them. We synthesize a series of homologous Pro-Pro-Aro containing peptides (modeled based on earlier studies) and investigate the relative populations of its four Xaa-Pro rotamers using extensive 1D and 2D NMR techniques including TOCSY, HSQC and ROESY. We find several drawbacks that make this a relatively deficient model. Firstly, their relative populations of the rotamers (the most important data for current investigation) cannot be determined with high fidelity as they are dependent on the solvent polarity, solute concentration and chemical shift degeneracy of crucial NMR signals for the rotamers. Importantly, the populations of a few rotamers are influenced by strong 13-membered ring backbone H-bonds. Notably, some of the cisPro rotamers do not even contain the inter-side chain assembly, whose nature is under investigation. Design of novel models – unconstrained by H-bonds We design the Acyl-Pro-Pro-Aro-OMe peptides that lack the possibility of forming the 13-membered ring H-bonded structures. Thorough 1D and 2D NMR analyses of these models reveal that strong Type VI β-turn type 10-membered ring H-bonds are formed in the rotamers of these models – hence precluding their applications for current study. Interestingly, the relative rotamer populations are strongly influenced by solvent polarity and are entirely different from those of the corresponding C-terminal amide models. We further discover that the Pro-Pro-Aro motif is not essential to express the inter-side chain interactions – Ala-Pro-Aro are sufficient. Formation of the 10-membered H-bonding interactions, however, are not precluded. Chapter 2: Design and Synthesis of Acyl-Pro-Phe-OMe: Novel models to investigate the role of HαXaa•••Aro interactions on Xaa-cisPro-Aro stability. Chapter 2 Section A: Design, Synthesis and Conformational Analysis of Ibu-Pro-Phe-OMe Chapter 2 is divided into two sections. In Section A, we replace the amino acid at the N-terminal of the putative Pro residue with simple isosteric isobutyryl group, the resulting minimalist dipeptide model shows the exclusive influence of desired inter-side chain interactions in the cisPro rotamer. Solvent polarity and temperature coefficient studies reveal that absence of any intramolecular H-bonding or Oπ* interactions in it. 1D and 2D NMR analyses clearly indicate the close proximity between the side chains of Ibu and Phe exclusively in the cisPro rotamer. The Kc/t value decreases upon mutation of Phe to Ala. All these features favor the Ibu-Pro-Phe-OMe as an ideal minimalistic model for investigating the nature of Ibu•••Ph assemblages in the cisPro rotamer. Chapter 2 Section B: Investigation of CH•••Aro /Alp•••Alp interactions in Ibu-cisPro-Xaa-OMe In Section B, the 1D and 2D NMR analyses of the complete set of the aliphatic and aromatic analogues Ibu-Pro-Xaa-OMe were investigated. DMSO-d6 was found to be the best solvent for mimicking both the folded and the unfolded local environments of these short peptide sequences. The HαIbu•••Aro assemblage is observed in Aro analogues, but cannot be electronically tuned. The aliphatic analogues also surprisingly contain the HαIbu•••Alp interactions! The Kc/t values (cisPro %) increase in the aliphatic analogues too, where the aliphatic side chain is long. Increase in cisPro stability is not due to ring current effects or intramolecular H-bonds or Oπ* interactions. It seems to be due to van der Waals type interactions between the involved side chains, either of which need not be aromatic in nature. Chapter 3: Nature of Inter-Side Chain Interactions at Acyl-cisPro-Aro Sequences: Evidence for van der Waals Interactions Chapter 3 Section A: Investigation of nature of inter-side chain interactions in R-CO-cisPro-Phe-OMe Chapter 3 has two sections. Section A describes the systematic design and synthesis of Acyl-Pro-Phe-OMe homologues where first the steric bulk and hence the surface area of the aliphatic side chain of the acyl group is varied. Interaction of the phenyl ring of Phe seems to occur with the Cα-Cβ σ-bond of the acyl group. Branching at either Cα or Cβ seems to destabilize the cisPro rotamer. Aliphatic•••Aromatic interactions overwhelm the cisPro rotamer population to be greater than that of transPro. In the analogues where the acidity of the acyl Cα-H bond is increased, the Kc/t does not increase correspondingly. The Δδ(trans-cis) ppm shifts of HαAcyl protons are dependent exclusively on its acidity rather than on the Kc/t values. In carbamyl-Pro, which entirely lack the HαAcyl proton, the Kc/t values are significantly high and improve as the aliphatic surface on the alkoxy group increases. Introduction of benzyloxy carbamyl group at Pro renders almost the same Kc/t values as that of ethyloxy carbamate. All these data contradict the C-H•••π interaction model and strongly support a van der Waals type interaction between the Acyl (preceding cisPro) group’s Xα-Yβ σ-bond and the Aro or Alp side chains (succeeding cisPro). Chapter 3 Section B: Evidence for the Van der Waals nature of Inter Side Chain (Acyl•••S.C.Aro/Alp) interactions- Determination of Interactions energies In Section B, a thorough investigation of both aliphatic•••aliphatic and aliphatic•••aromatic interactions on the background of homologous Acyl-Pro-Aro/Alp-OMe peptide models is undertaken. These models uniquely allow the delineation of contribution of the van der Waals interactions and the ring current effects to the cis/trans isomerization in these peptides. We see that the energy of the van der Waals component of these aliphatic•••aliphatic and aliphatic…aromatic interactions increase linearly with increase in Kc/t, in both DMSO-d6 and D2O. On other hand, energy from the ring current effects largely remains invariant. The Acyl•••Aro/Alp interactions are not hydrophobic and are facilitated by conformational effects. Chapter 4: Crystallographic evidence for van der Waals interaction-mediated stabilization of cisPro conformers Chapter 4 Section A: Systematic crystallization and crystal structure analyses of homologous Xaa-cisPro-Alp and Xaa-cisPro-Aro rotamers: Evidence for van der Waals interactions Chapter 4 has two sections, both of which present crystallographic evidence for the van der Waals nature of the Xaa•••Aro interactions at Xaa-cisPro-Aro sequences. Section A describes the unique crystal structures of five of the Acyl-Pro-Alp-OMe analogues that have been synthesized in the current study. All of them remarkably crystallize with two features: 1) the Acyl-Pro peptide bond adopts the cisPro rotamer in all; and 2) the aliphatic side chains of the acyl group and the Alp side chain are involved in van der Waals type interactions. The cisPro rotamers of even the bulkiest motifs, namely Ibu-Pro-Val-OMe, Piv-Pro-Ile-OMe and Piv-Pro-Leu-OMe crystallize, stabilized by van der Waals packing between aliphatic groups of the acyl and the Leu/Ile/Val side chains. Where the side chains are not long enough to make sub-van der Waals contacts with each other, their acyl C′-Cα σ-bond rotations are restricted due to Oσ* interactions involving the charge on the acyl carbonyl O. Where this occurs, the short space between the acyl and Alp side chains are filled in by aliphatic groups from neighbouring molecules at sub van der Waals distances. The Pro, Alp and χ1(Alp) dihedral angles are restricted to narrow range of values, irrespective of the length of Alp side chain, indicating that this backbone conformation is a conformational minimum when i+3i backbone H-bond is removed, with Pro at the i+1st position. This is further substantiated in Piv-Pro-Gly-OMe, which crystallizes in trans-Pro form, but still adopts similar backbone dihedral angles in spite of lacking any Alp side chain for interactions with the acyl group. Three of the Acyl-Pro-Aro-OMe models also crystallize in cisPro rotamer forms – both exhibit van der Waals type contacts between the Acyl group and backbone of Phe, rather than the aromatic ring of Phe. The phenyl ring of Phe may or may not form intramolecular Ph•••Pro inter-side chain contacts – which is not a pre-requisite for cisPro stabilization. No C-H••• interactions are observed anywhere in these peptides – van der Waals type contacts alone predominate in all cases. There are no abnormal distortions in bond angles or lengths even in the most sterically hindered cases, signifying that the conformations of these cisPro rotamers involving aliphatic•••aliphatic type contacts are natural minima. Chapter 4 Section B: Mining the PDB for Statistical Evidence of van der Waals interactions Section B of chapter 4 describes the data mining and statistical analyses of Xaa-cisPro-Phe, Xaa-cisPro-Val and Xaa-cisProLeu sequences in the PDB. The PEARL program was used to mine the PDB data. The overall frequency of 5.3% for appearance of cisPro among all Xaa-Pro peptide bonds, improves when Xaa is Phe or Tyr. However, several anomalies highlight the need for refining the analyses set to only those sequences where the side chains of Xaa and Aro/Alp face each other. In this refined set, clearly, inter side chain Xaa•••Alp/Aro contacts take precedence over even Aro•••Pro interactions at Aro-cisPro sequences (where Xaa is Aro). The Phe and the Leu side chains induce similar conformational effects on the preceding Xaa-Pro backbone. So does Val. Strong aliphatic•••aliphatic inter side chain contacts at van der Waals distances are observed to flank cisPro in several proteins. Substitution at the Cα of Xaa governs the proximity of the approaching side chain of Alp / Aro residue. The Cα-H of Xaa steers away from the Aro side chain at Xaa-Pro-Phe sequences, as the Aro group gets closer to it – implying the absence of ordered C-H••• contacts between them. There is consistent parallel alignment between Cα-Cβ -bond of Xaa and the C -C bond of the approaching side chain of Alp or Aro group – clearly highlighting the presence of van der Waals type interactions between them. All these evidences clearly point towards the van der Waals nature of local interactions at cisPro-Aro/Alp peptide sequences. Chapter 5: A novel 4-carbon covalent surrogate model for peptide H-Bond Chapter 5 describes the design and synthesis of novel 4-carbon covalent surrogates for the peptide H-bond (HBS). These surrogates would allow the unique constraining of two peptide strands in their extended conformations. The covalent HBS contain four orthogonal functional groups for independent extension at all of the four ends – similar to an endogenous inter-strand peptide H-bond. The synthesis of the surrogate is achieved by directly using natural chiral amino acid derivatives, beginning from amino alcohols obtained from reduction of desired amino acids. Suitably N-protected alcohols undergo oxidation to aldehyde followed by Grignard addition of allyl magnesium bromide, TBDMS protection of the homoallylic alcohol and reductive ozonolysis of the olefin to get a primary alcohol which is subject to Fukuyama-Mitsunobu reaction with desire protected peptide. The residue preferences that produce strongest inter-strand H-bonds were explored. The designed 4-carbon covalent HBS was incorporated using this methodology in a Gramicidin-S analogue, its first structural mimic containing only a single turn motif. This HBS model will have wide applications for constraining peptides in a number of secondary structures.

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