List of Figures Figure No. Figure Caption Page No. Figure 1.1. Cation- interactions and their modulations. 4 Figure 1.2. Three conformations of benzene dimer, S is not a minimum on the potential energy surface. 7 Figure 1.3. The cation-alkane interactions. 10 Figure 1.4. The graphical representation of components of interaction energy as depicted by energy decomposition analysis. 31 Figure 2.1. The MP2/6-31G* structures of the various metal ion complexes of ethylene and methyl substituted ethylene. Point group of the structure, complexation energy (in kcal/mol), distance between metal ion and sp 2 carbon and the C=C bond length are provided below each structure. The distances are given in Å units. 61 Figure 2.2. The MP2/6-31G* structures of the various metal ion complexes of cycloalkenes and its methyl substituted analogues. Point group of the structure, complexation energy (in kcal/mol), distance between the metal ion and C=C midpoint and the C=C bond length (in bold) are provided with each structure. The distances are given in Å units. 63 Figure 2.3. (a) A plot of the complexation energy (kcal/mol) of various metal ion alkene complexes. (b) The complexation energy (kcal/mol) versus the charge transfer (au) from the alkene to the metal ion. (c) The polarisability of the alkenes (au). (d) The complexation energy (kcal/mol) versus the electron density (au) at the intermolecular bond critical point. 64 Figure 2.4. The energetic components of the HF/6-31G* complexation energy (kcal/mol) of metal ion alkene complexes studied through a reduced variational space analysis on the MP2/6-31G* structures. 70 Figure 2.5. The correlation between sum of charge transfer components (CT M-A + CT A-M ) in the complexation energy (kcal/mol) versus the elongation of C=C bond (Å) due to Cu + binding. 71 Figure 2.6. The relative orbital energies (in ev) diagram of the HOMOs of the various alkenes (left), the LUMOs of the various metal ions (right) and the HOMOs and LUMOs of the ethylene complexes (centre). 72 Figure 3.1. The possible conformations of Li + -methane and Li + -ethane complexes. 87 Figure 3.2. The comparison of complexation energies with CCSD(T)/CBS results. 90 Figure 3.3. The minimum energy structures of Li + -alkane complexes. The C-C bond length and the shortest Li +... C distance in the complex have i
been given in Å units. 93 Figure 3.4. The MP2/cc-pVTZ complexation energies (kcal/mol) of cationalkane complexes. 93 Figure 3.5 The structures of (Li + -ethane) water systems, and the plot (bottom) of Li + -ethane binding energies (kcal/mol) with respect to the systematic solvation by water molecules at alkane side and at cation side. The geometries are given in Å units. 94 Figure 3.6. The DFT-SAPT results (kcal/mol) of Li + -alkane and Mg 2+ -alkane complexes. 96 Figure 3.7. The complexation energy components of M-A2 (a) and M-cA6 (b) and difference of the complexation energy components of cation- and cation-alkane systems, (a ) E = E M-E2 E M-A2 ; (b ) E = E M- ce6 E M-cA6 ) (BE obtained from the CCSD(T)/CBS results have been showed except for Ca 2+ complexes, for Ca 2+ complexes the MP2/ccpVTZ results have been showed. The numbers are expressed in kcal/mol units. 98 Figure 3.8. The MP2/cc-pVTZ electron density (au) obtained at (3, -1) intermolecular bond critical bond, for Cu + and Zn 2+ complexes 6-311++G** basis set has been used. 100 Figure 4.1. The comparative representation of strength (kcal/mol) of covalent and noncovalent bonds. 109 Figure 4.2. The various metal ions considered from the periodic table for the study. 109 Figure 4.3. The distance between metal ion to CC bond center of M-H1, M-H2 and M-H3, and metal ion to midpoint of Bz and Cp obtained at B3LYP/def2-SVP level, all the numbers are expressed in Å units. 114 Figure 4.4. The various binding preferences of TM-H1 complexes observed in the study. 116 Figure 4.5. The various preferences (hapticity) of metal ion binding to M-Cp complexes and the geometrical description for the preference of metal ion. 118 Figure 4.6. The various mode of transition metal ion binding in M-Bz complexes. 122 Figure 4.7. The distance between transition metal ion to midpoint of CC bond (H1, H2, H3) or midpoint of ring carbons (Bz and Cp) for monocationic (a, c, e, g, i) and dicationic (b, d, f, h, j) complexes obtained at B3LYP/def2-SVP level, all the numbers are expressed in Å units. The circle in the plots represent the low spin complexes, and the cross mark (X) on the lines indicates the unbound complexes which are not located in the stationary point or ɳ 1, ɳ 2, ɳ 3-2 type of binding with ethane (in the plots of M-H1 complexes). 124 ii
Figure 4.8. The distance between metal ion (p-block) to midpoint of CC bond (H1, H2, H3) or midpoint of ring carbons (Bz and Cp) mono (a) and dicationic (b) complexes obtained at B3LYP/def2-SVP level, all the numbers are expressed in Å units. The cross mark (X) on the lines indicates that the corresponding unbound complexes which are not located in the stationary point. 126 Figure 4.9. The B3LYP/def2-SVP complexation energies (kcal/mol) of monocationic systems considered in the study. 129 Figure 4.10. The B3LYP/def2-SVP complexation energies (kcal/mol) of dicationic systems considered in the study. 129 Figure 4.11. TM-hydrocarbon complexes atomic positions and (3,-1) bond critical points. 133 Figure 4.12. Diagrams showing the relationship between electron density and the complexation energy. The fourth row monocationic complexes of M-H1, M-H2, MH3, M-Bz and M-Cp. 134 Figure 4.13. The components of complexation energies (kcal/mol) of K +, Cu + and Ga + (right side) Ca 2+, Zn 2+ and Ge 2+ (left side) hydrocarbon complexes. 137 Figure 5.1. The comparison of binding energies (kcal/mol) obtained at M06-2X/cc-pVTZ, MP2/cc-pVTZ and PBEO/cc-pVDZ methods for hydrocarbon dimers. 148 Figure 5.2. The representative acyclic and cyclic Li + bound hydrocarbon dimers and the principal geometries (Å) obtained at M06-2X/6-31G* level of theory. 157 Figure 5.3. The representative acyclic and cyclic metalated hydrocarbon dimers with their binding energies (kcal/mol) and the principal geometries obtained at M06-2X/6-31G* level of theory. 158 Figure 5.4. Atomic positions and critical points of acyclic hydrocarbon dimers (a) A-A (b) E-E (c) A-E. BCPs are represented by red color dots and CCPs are represented by green color dots and RCPs are represented by yellow color obtained at M06-2X/cc-pVTZ. 160 Scheme 2.1. The various alkenes (methyl substituted ethylene, cycloalkenes and dimethyl substituted cycloalkenes) and metal ions considered for the study. 58 Scheme 3.1. The cation-alkane and cation- systems considered for the study. 85 Scheme 4.1. The hydrocarbons considered for the study. 112 Scheme 5.1. A schematic representation of the acyclic saturated (An), acyclic unsaturated (En), cyclic saturated (can), and cyclic unsaturated (cen) model hydrocarbons considered in this study. 145 Scheme 5.2. The schematic representation of M-hydrocarbon-hydrocarbon and sandwich complexes of a metal ion. 156 iii
List of Tables Table No. Table 1.1. Table 2.1. Table 2.2. Table 2.3. Table 2.4. Table 2.5. Table 2.6. Table 3.1. Table 3.2. Table 3.3. Table 4.1. Table 4.2. Page Table Caption No. The relation between the molecular orbital space and energy components in the RVS SCF calculations in a binary system. The subscript occ. and vir refer to the occupied and virtual fragment orbitals. Brackets around an orbital subset name indicate that the subset is frozen in the calculation. 32 BSSE corrected complexation energies (kcal/mol) of the ethylene complexes at different levels of theory using the 6-311++G** basis set on MP2/6-31G* structures. 62 The difference in complexation energies (kcal/mol) of cycloalkenes and their methyl substituted analogs. 64 The reorganization energy (kcal/mol) of various cation-alkene complexes. 66 The change in the percentage of complexation energy components as size of alkene increases from 1 to 11 (it is calculated by [(comp 1 - comp 11 )/comp 1 x100]). The percentages in negative sign are underlined and indicate that the contribution of specific energy component decrease as size of alkene increases. 69 The MP2/6-311++G** occupation number of the C=C bond in cis/trans-2-butene complexes. 73 The effect of the size of the π-system in cation alkene complexes by MP2/6-311++G** electron density (ρ in a.u.) and the distance (Å) between the metal ion to the C=C bond midpoint. 75 The details of conformational analysis and the experimental and calculated values used in this study for alkanes. 88 The complexation energies (kcal/mol) were evaluated at MP2/ccpVTZ//MP2/cc-pVTZ (A) and MP2/cc-pVTZ//B3LYP/6-31G* (B) methods; the difference between them (A-B) called as diff. 89 The percentage contribution of complexation energy components obtained from RVS and DFT-SAPT energy decomposition analysis schemes. 99 The spin multiplicity (2S+1; S-Total spin) assigned for the high spin (HS) and low spin (LS) complexes of transition metal ions. 112 The comparison of principal geometries of M-H2 complexes (M=alkali metal ions) obtained from B3LYP/6-31G*, B3LYP/def-2-SVP and B3LYP/def2-TZVP methods. 113 iv
Table 4.3. The transition metal ion complexes obtained as low spin configuration prefers over the corresponding high spin complex. 115 Table 4.4. The unbound transition metal ion complexes of various hydrocarbons. 116 Table 4.5. The spin density (SD, au) and the geometrical parameter (Å), d CC bond length, r M-C distance of monocationic M-Cp complexes. 119 Table 4.6. The spin density (SD, au) and the geometrical parameter (Å), d CC bond length, r M-C distances of dicationic M-Cp complexes. 120 Table 4.7. The Mulliken charges with summed hydrogen ( 1-CH1, 2-CH2, 3-CH3, 4- CH4 and 5-CH5) and charge on metal ion ( M) and the distance between metal ion to carbon (Å). 121 Table 4.8. The binding preference of transition metal ions in M-Bz complexes. 122 Table 4.9. The comparison of DFT and ab initio complexation energies (kcal/mol) of M-H2 complexes obtained at MP2 level using B3LYP/def2-SVP structures. 128 Table 4.10. The reorganisation energies (kcal/mol) of various metal ionhydrocarbon complexes obtained at B3LYP/def2-SVP level of theory. 131 Table 5.1. DFT and ab initio binding energies (kcal/mol) of cyclo-hexane and benzene dimers. 150 Table 5.2. The M06-2X/cc-pVTZ//M06-2X/6-31G* binding energies (kcal/mol) for the various hydrocarbon dimer considered in the study. 151 Table 5.3. The E cat values (kcal/mol) calculated and the charge transfer (au) calculated with the natural charges. The values are obtained at M06-2X/cc-pVTZ level of theory. 158 Table 5.4. The M06-2X/cc-pVTZ electron density and the laplacian of the electron density at (3,-1) intermolecular bond critical point, the values are expressed in au. 159 Table 5.5. The DFT-SAPT results (kcal/mol) of acyclic and cyclic hydrocarbon dimers. 162 v